EBK THOMAS' CALCULUS
14th Edition
ISBN: 9780134654874
Author: WEIR
Publisher: VST
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Chapter 16.7, Problem 7E
To determine
Find the circulation of the
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Don't do 14. Please solve 19
Please solve 14 and 15
1. Consider the following system of equations:
x13x2 + 4x3 - 5x4 = 7
-2x13x2 + x3 - 6x4 = 7
x16x213x3 - 21x4 = 28
a) Solve the system. Write your solution in parametric and vector form.
b) What is a geometric description of the solution.
7
c) Is v =
7 in the span of the set S=
[28.
1
HE
3
-5
3
·6
? If it is, write v
6
as a linear combination of the vectors in S. Justify.
d) How many solutions are there to the associated homogeneous system for
the system above? Justify.
e) Let A be the coefficient matrix from the system above. Find the set of all
solutions to Ax = 0.
f) Is there a solution to Ax=b for all b in R³? Justify.
Chapter 16 Solutions
EBK THOMAS' CALCULUS
Ch. 16.1 - Match the vector equations in Exercises 1–8 with...Ch. 16.1 - Match the vector equations in Exercises 1–8 with...Ch. 16.1 - Match the vector equations in Exercises 1–8 with...Ch. 16.1 - Match the vector equations in Exercises 1–8 with...Ch. 16.1 - Match the vector equations in Exercises 1–8 with...Ch. 16.1 - Prob. 6ECh. 16.1 - Prob. 7ECh. 16.1 - Match the vector equations in Exercises 1–8 with...Ch. 16.1 - Evaluate ∫C (x + y) ds, where C is the...Ch. 16.1 - Evaluate ∫C (x − y + z − 2) ds, where C is the...
Ch. 16.1 - Evaluate ∫C (xy + y + z) ds along the curve r(t) =...Ch. 16.1 - Evaluate along the curve r(t) = (4 cos t)i + (4...Ch. 16.1 - Prob. 13ECh. 16.1 - Find the line integral of over the curve r(t) =...Ch. 16.1 - Integrate over the path C1 followed by C2 from...Ch. 16.1 - Integrate over the path C1 followed by C2...Ch. 16.1 - Integrate f(x, y, z) = (x + y + z)/(x2 + y2 + z2)...Ch. 16.1 - Integrate over the circle r(t) = (a cos t)j + (a...Ch. 16.1 - Evaluate ∫C x ds, where C is
the straight-line...Ch. 16.1 - Evaluate , where C is
the straight-line segment x...Ch. 16.1 - Find the line integral of along the curve r(t) =...Ch. 16.1 - Find the line integral of f(x, y) = x − y + 3...Ch. 16.1 - Evaluate , where C is the curve x = t2, y = t3,...Ch. 16.1 - Find the line integral of along the curve , 1/2 ≤...Ch. 16.1 - Evaluate ,where C is given in the accompanying...Ch. 16.1 - Evaluate , where C is given in the accompanying...Ch. 16.1 - Prob. 27ECh. 16.1 - Prob. 28ECh. 16.1 - In Exercises 27–30, integrate f over the given...Ch. 16.1 - In Exercises 27–30, integrate f over the given...Ch. 16.1 - Prob. 31ECh. 16.1 - Find the area of one side of the “wall” standing...Ch. 16.1 - Mass of a wire Find the mass of a wire that lies...Ch. 16.1 - Center of mass of a curved wire A wire of density ...Ch. 16.1 - Mass of wire with variable density Find the mass...Ch. 16.1 - Center of mass of wire with variable density Find...Ch. 16.1 - Moment of inertia of wire hoop A circular wire...Ch. 16.1 - Inertia of a slender rod A slender rod of constant...Ch. 16.1 - Two springs of constant density A spring of...Ch. 16.1 - Wire of constant density A wire of constant...Ch. 16.1 - Prob. 41ECh. 16.1 - Center of mass and moments of inertia for wire...Ch. 16.2 - Find the gradient fields of the functions in...Ch. 16.2 - Find the gradient fields of the functions in...Ch. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5ECh. 16.2 - Prob. 6ECh. 16.2 - In Exercises 7−12, find the line integrals of F...Ch. 16.2 - Prob. 8ECh. 16.2 - In Exercises 7−12, find the line integrals of F...Ch. 16.2 - In Exercises 7−12, find the line integrals of F...Ch. 16.2 - Prob. 11ECh. 16.2 - Line Integrals of Vector Fields
In Exercises 7−12,...Ch. 16.2 - In Exercises 13–16, find the line integrals along...Ch. 16.2 - In Exercises 13–16, find the line integrals along...Ch. 16.2 - In Exercises 13–16, find the line integrals along...Ch. 16.2 - In Exercises 13–16, find the line integrals along...Ch. 16.2 - Prob. 17ECh. 16.2 - Along the curve , , evaluate each of the following...Ch. 16.2 - In Exercises 19–22, find the work done by F over...Ch. 16.2 - In Exercises 19–22, find the work done by F over...Ch. 16.2 - In Exercises 19–22, find the work done by F over...Ch. 16.2 - In Exercises 19–22, find the work done by F over...Ch. 16.2 - Evaluate along the curve from (–1, 1) to (2,...Ch. 16.2 - Prob. 24ECh. 16.2 - Evaluate for the vector field along the curve ...Ch. 16.2 - Prob. 26ECh. 16.2 - Prob. 27ECh. 16.2 - Prob. 28ECh. 16.2 - Circulation and flux Find the circulation and flux...Ch. 16.2 - Flux across a circle Find the flux of the...Ch. 16.2 - Prob. 31ECh. 16.2 - In Exercises 31–34, find the circulation and flux...Ch. 16.2 - In Exercises 31–34, find the circulation and flux...Ch. 16.2 - In Exercises 31–34, find the circulation and flux...Ch. 16.2 - Flow integrals Find the flow of the velocity field...Ch. 16.2 - Flux across a triangle Find the flux of the field...Ch. 16.2 - Prob. 37ECh. 16.2 - The flow of a gas with a density of over the...Ch. 16.2 - Find the flow of the velocity field F = y2i + 2xyj...Ch. 16.2 - Prob. 40ECh. 16.2 - Prob. 41ECh. 16.2 - Prob. 42ECh. 16.2 - Prob. 43ECh. 16.2 - Prob. 44ECh. 16.2 - Prob. 45ECh. 16.2 - Prob. 46ECh. 16.2 - Prob. 47ECh. 16.2 - Prob. 48ECh. 16.2 - A field of tangent vectors
Find a field G = P(x,...Ch. 16.2 - A field of tangent vectors
Find a field G = P(x,...Ch. 16.2 - Unit vectors pointing toward the origin Find a...Ch. 16.2 - Prob. 52ECh. 16.2 - Prob. 53ECh. 16.2 - Prob. 54ECh. 16.2 - Prob. 55ECh. 16.2 - Prob. 56ECh. 16.2 - In Exercises 55–58, F is the velocity field of a...Ch. 16.2 - In Exercises 55–58, F is the velocity field of a...Ch. 16.2 - Circulation Find the circulation of F = 2xi + 2zj...Ch. 16.2 - Prob. 60ECh. 16.2 - Flow along a curve The field F = xyi + yj − yzk is...Ch. 16.2 - Flow of a gradient field Find the flow of the...Ch. 16.3 - Which fields in Exercises 1–6 are conservative,...Ch. 16.3 - Which fields in Exercises 1–6 are conservative,...Ch. 16.3 - Which fields in Exercises 1–6 are conservative,...Ch. 16.3 - Which fields in Exercises 1–6 are conservative,...Ch. 16.3 - Which fields in Exercises 1−6 are conservative,...Ch. 16.3 - Which fields in Exercises 1−6 are conservative,...Ch. 16.3 - Finding Potential Functions
In Exercises 7–12,...Ch. 16.3 -
In Exercises 7–12, find a potential function f...Ch. 16.3 - In Exercises 7–12, find a potential function f for...Ch. 16.3 - In Exercises 7–12, find a potential function f for...Ch. 16.3 - In Exercises 7–12, find a potential function f for...Ch. 16.3 - In Exercises 7–12, find a potential function f for...Ch. 16.3 - Prob. 13ECh. 16.3 - In Exercises 13–17, show that the differential...Ch. 16.3 - Prob. 15ECh. 16.3 - In Exercises 13–17, show that the differential...Ch. 16.3 - In Exercises 13–17, show that the differential...Ch. 16.3 - Prob. 18ECh. 16.3 -
Although they are not defined on all of space R3,...Ch. 16.3 - Although they are not defined on all of space R3,...Ch. 16.3 - Prob. 21ECh. 16.3 - Prob. 22ECh. 16.3 - Prob. 23ECh. 16.3 - Evaluate
along the line segment C joining (0, 0,...Ch. 16.3 - Independence of path Show that the values of the...Ch. 16.3 - Prob. 26ECh. 16.3 - Prob. 27ECh. 16.3 - In Exercises 27 and 28, find a potential function...Ch. 16.3 - Work along different paths Find the work done by F...Ch. 16.3 - Work along different paths Find the work done by F...Ch. 16.3 - Evaluating a work integral two ways Let F =...Ch. 16.3 - Integral along different paths Evaluate the line...Ch. 16.3 - Exact differential form How are the constants a,...Ch. 16.3 - Prob. 34ECh. 16.3 - Prob. 35ECh. 16.3 - Prob. 36ECh. 16.3 - Prob. 37ECh. 16.3 - Gravitational field
Find a potential function for...Ch. 16.4 - In Exercises 1–6, find the k-component of curl(F)...Ch. 16.4 - Prob. 2ECh. 16.4 - In Exercises 1–6, find the k-component of curl(F)...Ch. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.4 - In Exercises 1–6, find the k-component of curl(F)...Ch. 16.4 - In Exercises 7–10, verify the conclusion of...Ch. 16.4 - In Exercises 7–10, verify the conclusion of...Ch. 16.4 - In Exercises 7–10, verify the conclusion of...Ch. 16.4 - In Exercises 7–10, verify the conclusion of...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - Prob. 20ECh. 16.4 - Find the counterclockwise circulation and outward...Ch. 16.4 - Find the counterclockwise circulation and the...Ch. 16.4 - Prob. 23ECh. 16.4 - Find the counterclockwise circulation of around...Ch. 16.4 - In Exercises 25 and 26, find the work done by F in...Ch. 16.4 - Prob. 26ECh. 16.4 - Apply Green’s Theorem to evaluate the integrals in...Ch. 16.4 - Apply Green’s Theorem to evaluate the integrals in...Ch. 16.4 - Apply Green’s Theorem to evaluate the integrals in...Ch. 16.4 - Prob. 30ECh. 16.4 - Prob. 31ECh. 16.4 - Prob. 32ECh. 16.4 - Use the Green’s Theorem area formula given above...Ch. 16.4 - Prob. 34ECh. 16.4 - Prob. 35ECh. 16.4 - Integral dependent only on area Show that the...Ch. 16.4 - Evaluate the integral
for any closed path C.
Ch. 16.4 - Evaluate the integral
for any closed path C.
Ch. 16.4 - Prob. 39ECh. 16.4 - Definite integral as a line integral Suppose that...Ch. 16.4 - Prob. 41ECh. 16.4 - Prob. 42ECh. 16.4 - Green’s Theorem and Laplace’s equation Assuming...Ch. 16.4 - Maximizing work Among all smooth, simple closed...Ch. 16.4 - Regions with many holes Green’s Theorem holds for...Ch. 16.4 - Prob. 46ECh. 16.4 - Prob. 47ECh. 16.4 - Prob. 48ECh. 16.5 - In Exercises 1–16, find a parametrization of the...Ch. 16.5 - In Exercises 1–16, find a parametrization of the...Ch. 16.5 - In Exercises 1–16, find a parametrization of the...Ch. 16.5 - In Exercises 1–16, find a parametrization of the...Ch. 16.5 - Prob. 5ECh. 16.5 - Prob. 6ECh. 16.5 - Prob. 7ECh. 16.5 - In Exercises 1–16, find a parametrization of the...Ch. 16.5 - Prob. 9ECh. 16.5 - Prob. 10ECh. 16.5 - Prob. 11ECh. 16.5 - Prob. 12ECh. 16.5 - Prob. 13ECh. 16.5 - In Exercises 1–16, find a parametrization of the...Ch. 16.5 - Prob. 15ECh. 16.5 - Prob. 16ECh. 16.5 - In Exercises 17–26, use a parametrization to...Ch. 16.5 - In Exercises 17–26, use a parametrization to...Ch. 16.5 - Prob. 19ECh. 16.5 - Prob. 20ECh. 16.5 - Prob. 21ECh. 16.5 - Prob. 22ECh. 16.5 - Prob. 23ECh. 16.5 - In Exercises 17–26, use a parametrization to...Ch. 16.5 - In Exercises 17–26, use a parametrization to...Ch. 16.5 - In Exercises 17–26, use a parametrization to...Ch. 16.5 - Prob. 27ECh. 16.5 - Prob. 28ECh. 16.5 - Prob. 29ECh. 16.5 - Prob. 30ECh. 16.5 - A torus of revolution (doughnut) is obtained by...Ch. 16.5 - Prob. 32ECh. 16.5 - Prob. 33ECh. 16.5 - Prob. 34ECh. 16.5 - Prob. 35ECh. 16.5 - Prob. 36ECh. 16.5 - Find the area of the surface cut from the...Ch. 16.5 - Find the area of the band cut from the paraboloid...Ch. 16.5 - Find the area of the region cut from the plane x +...Ch. 16.5 - Find the area of the portion of the surface x2 –...Ch. 16.5 - Prob. 41ECh. 16.5 - Prob. 42ECh. 16.5 - Find the area of the ellipse cut from the plane z...Ch. 16.5 - Find the area of the upper portion of the cylinder...Ch. 16.5 - Prob. 45ECh. 16.5 - Prob. 46ECh. 16.5 - Prob. 47ECh. 16.5 - Find the area of the surface 2x3/2 + 2y3/2 – 3z =...Ch. 16.5 - Prob. 49ECh. 16.5 - Prob. 50ECh. 16.5 - Prob. 51ECh. 16.5 - Prob. 52ECh. 16.5 - Prob. 53ECh. 16.5 - Find the area of the surfaces in Exercises...Ch. 16.5 - Use the parametrization
and Equation (5) to...Ch. 16.5 - Prob. 56ECh. 16.6 - In Exercises 1–8, integrate the given function...Ch. 16.6 - In Exercises 1–8, integrate the given function...Ch. 16.6 - In Exercises 1–8, integrate the given function...Ch. 16.6 - In Exercises 1–8, integrate the given function...Ch. 16.6 - Prob. 5ECh. 16.6 - Prob. 6ECh. 16.6 - Prob. 7ECh. 16.6 - In Exercises 1–8, integrate the given function...Ch. 16.6 - Integrate G(x, y, z) = x + y + z over the surface...Ch. 16.6 - Integrate G(x, y, z) = y + z over the surface of...Ch. 16.6 - Prob. 11ECh. 16.6 - Prob. 12ECh. 16.6 - Integrate G(x, y, z) = x + y + z over the portion...Ch. 16.6 - Prob. 14ECh. 16.6 - Prob. 15ECh. 16.6 - Prob. 16ECh. 16.6 - Prob. 17ECh. 16.6 - Prob. 18ECh. 16.6 - In Exercises 19–28, use a parametrization to find...Ch. 16.6 - In Exercises 19–28, use a parametrization to find...Ch. 16.6 - Prob. 21ECh. 16.6 - Prob. 22ECh. 16.6 - Prob. 23ECh. 16.6 - Prob. 24ECh. 16.6 - In Exercises 19–28, use a parametrization to find...Ch. 16.6 - In Exercises 19–28, use a parametrization to find...Ch. 16.6 - In Exercises 19–28, use a parametrization to find...Ch. 16.6 - Prob. 28ECh. 16.6 - Prob. 29ECh. 16.6 - Prob. 30ECh. 16.6 - In Exercises 31–36, use Equation (7) to find the...Ch. 16.6 - Prob. 32ECh. 16.6 - Prob. 33ECh. 16.6 - Prob. 34ECh. 16.6 - Prob. 35ECh. 16.6 - In Exercises 31–36, use Equation (7) to find the...Ch. 16.6 - Find the flux of the field through the surface...Ch. 16.6 - Find the flux of the field F(x, y, z) = 4xi + 4yj...Ch. 16.6 - Let S be the portion of the cylinder y = ex in the...Ch. 16.6 - Let S be the portion of the cylinder y = ln x in...Ch. 16.6 - Find the outward flux of the field F = 2xyi+ 2yzj...Ch. 16.6 - Find the outward flux of the field F = xzi + yzj +...Ch. 16.6 - Prob. 43ECh. 16.6 - Prob. 44ECh. 16.6 - Prob. 45ECh. 16.6 - Conical surface of constant density Find the...Ch. 16.6 - Prob. 47ECh. 16.6 - Prob. 48ECh. 16.6 - Prob. 49ECh. 16.6 - A surface S lies on the paraboloid directly above...Ch. 16.7 - In Exercises 1–6, find the curl of each vector...Ch. 16.7 - Prob. 2ECh. 16.7 - In Exercises 1–6, find the curl of each vector...Ch. 16.7 - Prob. 4ECh. 16.7 - Prob. 5ECh. 16.7 - Prob. 6ECh. 16.7 - In Exercises 7–12, use the surface integral in...Ch. 16.7 - Prob. 8ECh. 16.7 - In Exercises 7–12, use the surface integral in...Ch. 16.7 - Prob. 10ECh. 16.7 - In Exercises 7–12, use the surface integral in...Ch. 16.7 - In Exercises 7–12, use the surface integral in...Ch. 16.7 - Let n be the unit normal in the direction away...Ch. 16.7 - Prob. 14ECh. 16.7 - Prob. 15ECh. 16.7 - Prob. 16ECh. 16.7 - Prob. 17ECh. 16.7 - Prob. 18ECh. 16.7 - In Exercises 19–24, use the surface integral in...Ch. 16.7 - In Exercises 19–24, use the surface integral in...Ch. 16.7 - In Exercises 19–24, use the surface integral in...Ch. 16.7 - Prob. 22ECh. 16.7 - Prob. 23ECh. 16.7 - In Exercises 19–24, use the surface integral in...Ch. 16.7 - Prob. 25ECh. 16.7 - Verify Stokes’ Theorem for the vector field F =...Ch. 16.7 - Prob. 27ECh. 16.7 - Prob. 28ECh. 16.7 - Prob. 29ECh. 16.7 - Prob. 30ECh. 16.7 - Prob. 31ECh. 16.7 - Prob. 32ECh. 16.7 - Prob. 33ECh. 16.7 - Prob. 34ECh. 16.8 - In Exercises 1–8, find the divergence of the...Ch. 16.8 - Prob. 2ECh. 16.8 - Prob. 3ECh. 16.8 - Prob. 4ECh. 16.8 - Prob. 5ECh. 16.8 - Prob. 6ECh. 16.8 - Prob. 7ECh. 16.8 - Prob. 8ECh. 16.8 - In Exercises 9–20, use the Divergence Theorem to...Ch. 16.8 - In Exercises 9–20, use the Divergence Theorem to...Ch. 16.8 - In Exercises 9–20, use the Divergence Theorem to...Ch. 16.8 - In Exercises 9–20, use the Divergence Theorem to...Ch. 16.8 - Prob. 13ECh. 16.8 - Prob. 14ECh. 16.8 - Prob. 15ECh. 16.8 - Prob. 16ECh. 16.8 - Prob. 17ECh. 16.8 - Prob. 18ECh. 16.8 - Prob. 19ECh. 16.8 - In Exercises 9–20, use the Divergence Theorem to...Ch. 16.8 - Prob. 21ECh. 16.8 - Prob. 22ECh. 16.8 - Prob. 23ECh. 16.8 - Prob. 24ECh. 16.8 - Prob. 25ECh. 16.8 - Prob. 26ECh. 16.8 - Prob. 27ECh. 16.8 - Prob. 28ECh. 16.8 - Prob. 29ECh. 16.8 - Prob. 30ECh. 16.8 - Prob. 31ECh. 16.8 - Prob. 32ECh. 16.8 - Prob. 33ECh. 16.8 - Prob. 34ECh. 16.8 - Prob. 35ECh. 16.8 - Prob. 36ECh. 16 - Prob. 1GYRCh. 16 - How can you use line integrals to find the centers...Ch. 16 - Prob. 3GYRCh. 16 - Prob. 4GYRCh. 16 - Prob. 5GYRCh. 16 - Prob. 6GYRCh. 16 - Prob. 7GYRCh. 16 - Prob. 8GYRCh. 16 - Prob. 9GYRCh. 16 - Prob. 10GYRCh. 16 - How do you calculate the area of a parametrized...Ch. 16 - Prob. 12GYRCh. 16 - What is an oriented surface? What is the surface...Ch. 16 - Prob. 14GYRCh. 16 - Prob. 15GYRCh. 16 - Prob. 16GYRCh. 16 - Prob. 17GYRCh. 16 - Prob. 18GYRCh. 16 - The accompanying figure shows two polygonal paths...Ch. 16 - The accompanying figure shows three polygonal...Ch. 16 - Integrate over the circle r(t) = (a cos t)j + (a...Ch. 16 - Prob. 4PECh. 16 - Evaluate the integrals in Exercises 5 and 6.
5.
Ch. 16 - Prob. 6PECh. 16 - Prob. 7PECh. 16 - Integrate F = 3x2yi + (x3 + l)j + 9z2k around the...Ch. 16 - Prob. 9PECh. 16 - Evaluate the integrals in Exercises 9 and...Ch. 16 - Prob. 11PECh. 16 - Prob. 12PECh. 16 - Prob. 13PECh. 16 - Hemisphere cut by cylinder Find the area of the...Ch. 16 - Prob. 15PECh. 16 - Prob. 16PECh. 16 - Circular cylinder cut by planes Integrate g(x, y,...Ch. 16 - Prob. 18PECh. 16 - Prob. 19PECh. 16 - Prob. 20PECh. 16 - Prob. 21PECh. 16 - Prob. 22PECh. 16 - Prob. 23PECh. 16 - Prob. 24PECh. 16 - Prob. 25PECh. 16 - Prob. 26PECh. 16 - Prob. 27PECh. 16 - Prob. 28PECh. 16 - Which of the fields in Exercises 29–32 are...Ch. 16 - Prob. 30PECh. 16 - Which of the fields in Exercises 29–32 are...Ch. 16 - Prob. 32PECh. 16 - Prob. 33PECh. 16 - Prob. 34PECh. 16 - In Exercises 35 and 36, find the work done by each...Ch. 16 - In Exercises 35 and 36, find the work done by each...Ch. 16 - Finding work in two ways Find the work done...Ch. 16 - Flow along different paths Find the flow of the...Ch. 16 - Prob. 39PECh. 16 - Prob. 40PECh. 16 - Prob. 41PECh. 16 - Prob. 42PECh. 16 - Prob. 43PECh. 16 - Prob. 44PECh. 16 - Prob. 45PECh. 16 - Prob. 46PECh. 16 - Prob. 47PECh. 16 - Moment of inertia of a cube Find the moment of...Ch. 16 - Use Green’s Theorem to find the counterclockwise...Ch. 16 - Prob. 50PECh. 16 - Prob. 51PECh. 16 - Prob. 52PECh. 16 - In Exercises 53–56, find the outward flux of F...Ch. 16 - In Exercises 53–56, find the outward flux of F...Ch. 16 - Prob. 55PECh. 16 - Prob. 56PECh. 16 - Prob. 57PECh. 16 - Prob. 58PECh. 16 - Prob. 59PECh. 16 - Prob. 60PECh. 16 - Prob. 1AAECh. 16 - Use the Green’s Theorem area formula in Exercises...Ch. 16 - Prob. 3AAECh. 16 - Use the Green's Theorem area formula in Exercises...Ch. 16 - Prob. 5AAECh. 16 - Prob. 6AAECh. 16 - Prob. 7AAECh. 16 - Prob. 8AAECh. 16 - Prob. 9AAECh. 16 - Prob. 10AAECh. 16 - Prob. 11AAECh. 16 - Prob. 12AAECh. 16 - Archimedes’ principle If an object such as a ball...Ch. 16 - Prob. 14AAECh. 16 - Faraday’s law If E(t, x, y, z) and B(t, x, y, z)...Ch. 16 - Prob. 16AAECh. 16 - Prob. 17AAECh. 16 - Prob. 18AAECh. 16 - Prob. 19AAECh. 16 - Prob. 20AAECh. 16 - Prob. 21AAE
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- 4. Suppose that A is made up of 5 column vectors in R³, and suppose that the rank(A)=3. a. How many solutions are there to Ax=0? Justify. b. What is a geometric description for the nullspace(A)? Justify. c. Do the column vectors of A span R³? Justify. d. Is A invertible? Justify.arrow_forward3. Suppose that A is 5 x 5 and rank(A)=4. Use this information to answer the following. a. Give a geometric description of nullspace(A). Justify. b. Is A invertible? Justify. c. Give a geometric description of the span of the column vectors of A. What space are the column vectors of A in? Justify. d. What is determinant of A? Justify.arrow_forward2. Consider the matrix: A || 1 1 -3 14 2 1 01 4 1 2 2 -26 1 -3 1 5] a) What is rank(A)? b) Is A invertible? Justify. c) Find the nullspace(A). Justify. d) Is the trivial solution the only solution to Ax=0? Justify. e) What is the span of the column vectors of A? Justify.arrow_forward
- E 5. Suppose that S={v € R²: v = [2x² - 3]}. Is S a subspace of R²? Prove or disprovearrow_forward6. Suppose that V1, V2 ER", show that span{v1, v2} is a subspace of Rn.arrow_forwardRa X 2) slots per pole per phase 3/31 180 Ko Sin (1) Kdl 1 sin (4) sin(3) Sin (30) اذا مرید شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 Fo lasa! G s.1000-950 20:05 1000 Capper losses: 5kw Rotor input lookw 0.05 ined sove in peaper I need a detailed solution on paper please 6) 1 ۳/۱ وه اذا ميريد شرح الكتب فقط look DC 7) rotov Find the general solution of the following equations: +4y=tan2x 3 7357 Find the general solution of the following equations: - Qll y + y (³) = 0. 101arrow_forward
- B: 18060 msl Kd Ka, Sin (n) I sin () sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 G 5005 1000 s = 1000-950 Copper bosses 5kW /0001 Rotor input 5 : loo kw 0.05 6) 1 اذا ميريد شرح الكتب فقط ١٥٠ 7) rotov DC ined sove in Deaper I need a detailed solution on paper please dy x+2y-4 = dx 2x-y-3 Find the general solution of the following equations: 02//yl-4y+13y=esinarrow_forward1) R₂ = X2 2) slots per pole per phase = 3/31 B msl kd 180 60 Kal Sin (1) I sin () sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 G 5005 1000 s = 1000-950 Copper bosses 5kW Rotor input: 5 0.05 loo kw 6) 1 /0001 اذا ميريد شرح الكتب فقط look 7) rotov DC ined sove in peaper I need a detailed solution on paper please Q1// Find the solution of: 'y' = x² +376 x4+316 xyo Q2 Find the solution of the initial-valued problems: ex-y y' +exarrow_forwardR₂ = X2 2) slots per pole per phase = 3/31 B-18060 msl kd Kasi Sin (1) I sin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed s = 1000-950 1000 Copper losses: 5kw Rotor input 5 0.05 6) 1 120 x 50 G loo kw ined sove in peaper I need a detailed solution on paper please Q3// x²y// +xy/ + (x² - ½) y = x³/². اذا ميريد شرح الكتب فقط look 7) rotor DC Q4// x²y// - (2x+x²)y/ + (2 + x)y = x³. dy 2x+2y+4 = dx 2x-y-3arrow_forward
- ۳/۱ R2X2 2) slots per pole per phase = 3/31 B, 18060 msl Kas Sin() 1sin() sin(30) Sin (30) kd اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speeds S = 1000-950 1000 Copper bosses 5kw 120*50 loca G Rotor input 5 loo kw 6) 1 0.05 اذا ميريد شرح الكتب فقط lookw 7) rotor DC ined sove in peaper I need a detailed solution on paper please 064 Q1// Find the solution of QI/Find the solution of Inxy= 7357 x+2y³ y' = xy3arrow_forwardR₂ = X2 2) slots per pole per phase 3/31 msl 180 60 Kd Ka Sin (1) Isin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120*50 1000 6 S = 1000-950 1000 Copper bosses: 5kw Rotor input 5 0.05 : loo kw 6) 1 اذا ميريد شرح الكتب فقط 100 7) rotor DC ined sove in peaper I need a detailed solution on paper please Find the general solution of the following equations: Q2lyl-4y+13y=esinx. Find the general solution of the following equations: " Qly (49) - 16y= 0. 151arrow_forward۳/۱ R₂ = X2 2) slots per pole per phase = 3/31 B-18060 msl kd Kasi Sin (1) I sin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed s = 1000-950 1000 Copper losses: 5kw Rotor input 5 0.05 6) 1 120 x 50 G loo kw اذا میرید شرح الكتب فقط look 7) rotor DC ined sove in peaper I need a detailed solution on paper dy please 04 12=-cosx.y + 2cosx with y(x) = 1 か 'Oy + xlny + xe")dx + (xsiny + xlnx +*dy=0. 01arrow_forward
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