ADVANCED ENGINEERING MATH W/ACCESS
10th Edition
ISBN: 9781119096023
Author: Kreyszig
Publisher: WILEY
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Chapter 9.5, Problem 25P
r(t) = [10 cos t, 1, 10 sin t], P: (6, 1, 8)
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11.9 Recall from Prob. 10.8, that the following system of equations
is designed to determine concentrations (the e's in g/m³) in a series
of coupled reactors as a function of amount of mass input to each
reactor (the right-hand sides are in g/day):
15c3cc33300
-3c18c26c3 = 1200
-4c₁₂+12c3 = 2400
Solve this problem with the Gauss-Seidel method to & = 5%.
9.8 Given the equations
10x+2x2-x3 = 27
-3x-6x2+2x3 = -61.5
x1 + x2 + 5x3 = -21.5
(a) Solve by naive Gauss elimination. Show all steps of the compu-
tation.
(b) Substitute your results into the original equations to check your
answers.
Page
of 2
ZOOM
+
1) Answer the following questions by circling TRUE or FALSE (No explanation or
work required).
i) If A
=
[1
-2
1]
0 1
6, rank(A) = 3. (TRUE FALSE)
LO
0
0]
ii) If S = {1,x,x², x³} is a basis for P3, dim(P3) = 4 with the standard operations.
(TRUE FALSE)
iii) Let u = (1,1) and v = (1,-1) be two vectors in R². They are orthogonal according
to the following inner product on R²: (u, v) = U₁V₁ + 2U2V2. ( TRUE FALSE)
iv) A set S of vectors in an inner product space V is orthogonal when every pair of
vectors in S is orthogonal. (TRUE FALSE)
v) Dot product of two perpendicular vectors is zero. (TRUE FALSE)
vi) Cross product of two perpendicular vectors is zero. (TRUE FALSE)
2) a) i) Determine which function(s) are solutions of the following linear differential
equation.
-
y (4) — 16y= 0
•
3 cos x
•
3 cos 2x
-2x
•
e
• 3e2x-4 sin 2x
ii) Find the Wronskian for the set of functions that you found from i) as the solution
of the differential equation above.
iii) What does the result…
Chapter 9 Solutions
ADVANCED ENGINEERING MATH W/ACCESS
Ch. 9.1 - Prob. 1PCh. 9.1 - Find the components of the vector v with initial...Ch. 9.1 - Prob. 3PCh. 9.1 - Prob. 4PCh. 9.1 - Find the components of the vector v with initial...Ch. 9.1 - Find the terminal point Q of the vector v with...Ch. 9.1 - Find the terminal point Q of the vector v with...Ch. 9.1 - Find the terminal point Q of the vector v with...Ch. 9.1 - Find the terminal point Q of the vector v with...Ch. 9.1 - Find the terminal point Q of the vector v with...
Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Prob. 13PCh. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Prob. 17PCh. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - What laws do Probs. 12–16 illustrate?
12. (a + b)...Ch. 9.1 - Prob. 20PCh. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Prob. 22PCh. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Equilibrium. Find v such that p, q, u in Prob. 21...Ch. 9.1 - Find p such that u, v, w in Prob. 23 and p are in...Ch. 9.1 - Unit vector. Find the unit vector in the direction...Ch. 9.1 - Restricted resultant. Find all v such that the...Ch. 9.1 - Prob. 30PCh. 9.1 - For what k is the resultant of [2, 0, −7], [1, 2,...Ch. 9.1 - If |p| = 6 and |q| = 4, what can you say about the...Ch. 9.1 - Same question as in Prob. 32 if |p| = 9, |q| = 6,...Ch. 9.1 - Relative velocity. If airplanes A and B are moving...Ch. 9.1 - Same question as in Prob. 34 for two ships moving...Ch. 9.1 - Prob. 36PCh. 9.1 - Prob. 37PCh. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Prob. 8PCh. 9.2 - Prob. 9PCh. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Prob. 11PCh. 9.2 - What does u • v = u • w imply if u = 0? If u ≠...Ch. 9.2 - Prove the Cauchy–Schwarz inequality.
Ch. 9.2 - Verify the Cauchy–Schwarz and triangle...Ch. 9.2 - Prob. 15PCh. 9.2 - Triangle inequality. Prove Eq. (7). Hint. Use Eq....Ch. 9.2 - Prob. 17PCh. 9.2 - Prob. 18PCh. 9.2 - Prob. 19PCh. 9.2 - Prob. 20PCh. 9.2 - Prob. 21PCh. 9.2 - Let a = [1, 1, 0], b = [3, 2, 1], and c = [1, 0,...Ch. 9.2 - Let a = [1, 1, 0], b = [3, 2, 1], and c = [1, 0,...Ch. 9.2 - Let a = [1, 1, 0], b = [3, 2, 1], and c = [1, 0,...Ch. 9.2 - What will happen to the angle in Prob. 24 if we...Ch. 9.2 - Prob. 26PCh. 9.2 - Addition law. cos (α − β) = cos α cos β + sin α...Ch. 9.2 - Prob. 28PCh. 9.2 - Prob. 29PCh. 9.2 - Prob. 30PCh. 9.2 - Prob. 31PCh. 9.2 - Prob. 32PCh. 9.2 - Prob. 33PCh. 9.2 - Prob. 34PCh. 9.2 - Prob. 35PCh. 9.2 - Prob. 36PCh. 9.2 - Prob. 37PCh. 9.2 - Prob. 38PCh. 9.2 - Prob. 39PCh. 9.2 - Prob. 40PCh. 9.3 - Prob. 1PCh. 9.3 - Prob. 2PCh. 9.3 - Prob. 3PCh. 9.3 - Prob. 4PCh. 9.3 - Prob. 5PCh. 9.3 - Prob. 6PCh. 9.3 - Prob. 7PCh. 9.3 - Prob. 8PCh. 9.3 - Prob. 9PCh. 9.3 - Prob. 11PCh. 9.3 - Prob. 12PCh. 9.3 - Prob. 13PCh. 9.3 - Prob. 14PCh. 9.3 - Prob. 15PCh. 9.3 - Prob. 16PCh. 9.3 - Prob. 17PCh. 9.3 - Prob. 18PCh. 9.3 - Prob. 19PCh. 9.3 - Prob. 20PCh. 9.3 - Prob. 21PCh. 9.3 - Prob. 22PCh. 9.3 - Prob. 23PCh. 9.3 - Prob. 25PCh. 9.3 - Prob. 26PCh. 9.3 - Prob. 27PCh. 9.3 - Prob. 28PCh. 9.3 - Prob. 29PCh. 9.3 - Prob. 30PCh. 9.3 - Prob. 31PCh. 9.3 - Prob. 32PCh. 9.3 - Prob. 33PCh. 9.3 - Prob. 34PCh. 9.4 - Prob. 1PCh. 9.4 - Prob. 2PCh. 9.4 - Prob. 3PCh. 9.4 - Prob. 4PCh. 9.4 - Prob. 5PCh. 9.4 - Prob. 6PCh. 9.4 - Prob. 7PCh. 9.4 - Prob. 9PCh. 9.4 - Prob. 10PCh. 9.4 - Prob. 11PCh. 9.4 - Prob. 12PCh. 9.4 - Prob. 13PCh. 9.4 - Prob. 14PCh. 9.4 - Prob. 15PCh. 9.4 - Prob. 16PCh. 9.4 - Prob. 17PCh. 9.4 - Prob. 18PCh. 9.4 - Prob. 19PCh. 9.4 - Prob. 20PCh. 9.4 - Prob. 22PCh. 9.4 - Prob. 23PCh. 9.4 - Prob. 24PCh. 9.5 - Prob. 1PCh. 9.5 - Prob. 2PCh. 9.5 - Prob. 3PCh. 9.5 - Prob. 4PCh. 9.5 - Prob. 5PCh. 9.5 - Prob. 6PCh. 9.5 - Prob. 7PCh. 9.5 - Prob. 8PCh. 9.5 - Prob. 9PCh. 9.5 - Prob. 10PCh. 9.5 - Prob. 11PCh. 9.5 - Prob. 12PCh. 9.5 - Prob. 13PCh. 9.5 - Prob. 14PCh. 9.5 - Prob. 15PCh. 9.5 - Prob. 16PCh. 9.5 - Prob. 17PCh. 9.5 - Prob. 18PCh. 9.5 - Prob. 19PCh. 9.5 - Prob. 20PCh. 9.5 - Prob. 21PCh. 9.5 - r(t) = [10 cos t, 1, 10 sin t], P: (6, 1, 8)Ch. 9.5 - r(t) = [cos t, sin t, 9t], P: (1, 0, 18)Ch. 9.5 - Prob. 27PCh. 9.5 - Prob. 29PCh. 9.5 - Prob. 30PCh. 9.5 - Prob. 31PCh. 9.5 - Prob. 32PCh. 9.5 - Prob. 33PCh. 9.5 - Prob. 34PCh. 9.5 - Prob. 35PCh. 9.5 - Prob. 36PCh. 9.5 - Prob. 37PCh. 9.5 - Prob. 38PCh. 9.5 - Prob. 43PCh. 9.5 - Prob. 44PCh. 9.5 - Prob. 45PCh. 9.5 - Prob. 46PCh. 9.5 - CURVATURE AND TORSION
47. Circle. Show that a...Ch. 9.5 - Prob. 48PCh. 9.5 - Prob. 49PCh. 9.5 - Prob. 50PCh. 9.5 - Prob. 51PCh. 9.5 - Prob. 52PCh. 9.5 - Prob. 53PCh. 9.5 - Prob. 54PCh. 9.5 - Prob. 55PCh. 9.7 - Prob. 1PCh. 9.7 - Prob. 2PCh. 9.7 - Prob. 3PCh. 9.7 - Prob. 4PCh. 9.7 - Prob. 5PCh. 9.7 - Prob. 6PCh. 9.7 - Prob. 7PCh. 9.7 - Prob. 8PCh. 9.7 - Prob. 9PCh. 9.7 - Prob. 10PCh. 9.7 - Prob. 11PCh. 9.7 - Prob. 12PCh. 9.7 - Prob. 13PCh. 9.7 - Prob. 14PCh. 9.7 - Prob. 15PCh. 9.7 - Prob. 16PCh. 9.7 - Prob. 17PCh. 9.7 - Prob. 18PCh. 9.7 - Prob. 19PCh. 9.7 - Prob. 20PCh. 9.7 - Prob. 21PCh. 9.7 - Prob. 22PCh. 9.7 - Prob. 23PCh. 9.7 - Prob. 24PCh. 9.7 - Prob. 25PCh. 9.7 - Prob. 26PCh. 9.7 - Prob. 28PCh. 9.7 - Prob. 29PCh. 9.8 - Prob. 1PCh. 9.8 - Prob. 2PCh. 9.8 - Prob. 3PCh. 9.8 - Prob. 4PCh. 9.8 - Prob. 5PCh. 9.8 - Prob. 6PCh. 9.8 - Prob. 7PCh. 9.8 - Prob. 8PCh. 9.8 - CAS EXPERIMENT. Visualizing the Divergence. Graph...Ch. 9.8 - Prob. 11PCh. 9.8 - Prob. 12PCh. 9.8 - Prob. 13PCh. 9.8 - Prob. 14PCh. 9.8 - Prob. 15PCh. 9.8 - Prob. 16PCh. 9.8 - Prob. 17PCh. 9.8 - Prob. 18PCh. 9.8 - Prob. 19PCh. 9.8 - Prob. 20PCh. 9.9 - Prob. 1PCh. 9.9 - Prob. 2PCh. 9.9 - Prob. 3PCh. 9.9 - Prob. 4PCh. 9.9 - Prob. 5PCh. 9.9 - Prob. 6PCh. 9.9 - Prob. 7PCh. 9.9 - Prob. 8PCh. 9.9 - Prob. 9PCh. 9.9 - Prob. 10PCh. 9.9 - Prob. 11PCh. 9.9 - Prob. 12PCh. 9.9 - Prob. 13PCh. 9.9 - Prob. 15PCh. 9.9 - Prob. 16PCh. 9.9 - Prob. 17PCh. 9.9 - Prob. 18PCh. 9.9 - Prob. 19PCh. 9.9 - Prob. 20PCh. 9 - Prob. 1RQCh. 9 - Prob. 2RQCh. 9 - Prob. 3RQCh. 9 - Prob. 4RQCh. 9 - Prob. 5RQCh. 9 - Prob. 6RQCh. 9 - Prob. 7RQCh. 9 - Prob. 8RQCh. 9 - Prob. 9RQCh. 9 - Prob. 11RQCh. 9 - Prob. 12RQCh. 9 - Prob. 13RQCh. 9 - Prob. 14RQCh. 9 - Prob. 15RQCh. 9 - Prob. 16RQCh. 9 - Prob. 17RQCh. 9 - Prob. 18RQCh. 9 - Prob. 19RQCh. 9 - Prob. 20RQCh. 9 - Prob. 21RQCh. 9 - Prob. 22RQCh. 9 - Prob. 23RQCh. 9 - Prob. 24RQCh. 9 - Prob. 25RQCh. 9 - Prob. 26RQCh. 9 - Prob. 27RQCh. 9 - Prob. 28RQCh. 9 - Prob. 29RQCh. 9 - Prob. 30RQCh. 9 - Prob. 31RQCh. 9 - Prob. 32RQCh. 9 - Prob. 33RQCh. 9 - Prob. 34RQCh. 9 - Prob. 35RQCh. 9 - Prob. 36RQCh. 9 - Prob. 37RQCh. 9 - Prob. 38RQCh. 9 - Prob. 39RQCh. 9 - Prob. 40RQ
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