If a vector field F (x+ 2y + az)f + (bx – 3y – 2)]+ (4x +cy+ 2z) k is irotational then the value of a, b,e are A. -4,-2,-1 B. -4,-2,1 C. 4.-2.-1 D. 4,2.-1

Q: Q5. Are the set of vectors {[0 2 1]",[1 1 1]", [3 2 1]", [3 0 1]"} linearly independent? Does the…

A: Set of vectors are linearly independent if there is no non-zero solution of c1,c2,c3,c4. If there is…

Q: One of the following vectors lies in span{ 2+x + x?, 3+x- 2x2} (A) 4+ x – 7r² (B) 4+ x – 4x? (C) 4 +…

A: Solve the following

Q: [1 2] 3 6 Let A = Write the vector u = (4,3) as u = u, + u„ where u̟ and un belong to the row space…

A: The given matrix is A=1236. Obtain the reduced row echelon form of matrix A as follows…

Q: Do only question 6

A: Evaluate fx​(3,1)Evaluate fy​(3,1)Find the derivative of f(x,y) with respect to x, treating y as a…

Q: Let B={(1,-2,0,-1), (0,1,0,3), (1,2,1.0)], and x=(4,3,-2,-5) Find [x]B Give your answer in the form…

A: B=1, -2, 0, -1, 0, 1, 0, 3, 1, 2, 1, 0x=4, 3, -2, -5

Q: 31. The vector perpendici:!at to both 3i –-6j – 4k and -3i + 2j + 2k is A A -4i + 6j + 12k B - 4i +…

A: Cross product

Q: - c(13, 23, 21, 27, 37, 52, 34, 42, 31, 40, 54, 30, 15, 35, 19, 23, 22, 18) Fine the vector y by the…

A: year x 1951 13 1952 23 1953 21 1954 27 1955 37 1956 52 1957 34 1958 42 1959 31…

Q: Do question 11

A: Step 1: Step 2: Step 3: Step 4:

Q: Do question two only

A: Step 1: Assign variablesFrom the givena=⟨4,6,9⟩b=⟨−6,−3,2⟩Let:xa = 4ya = 6za = 9xb = -6yb = -3zb = 2…

Q: 3- The vectors x, = R3, are linearly independent. (1,0,1), x2 = (-1,0,1) and x3 = (-2,4, –3) in O…

A:

Q: Let T: R² → R² be a reflection in the x-axis. Find the image of each vector. (a) (2,7) (b) (6, -8)…

A: T: R2 - >  R2 is a inear map which is basically reflection in the x Axis. Therefore for any point…

Q: Do question 12 only

A: The given in item #12 is:∫04π​​∫01​∫0x2​xcos(y) dz dx dy Consider the innermost…

Q: Do only question 5

A: Step 1:Identify the variable you're differentiating with respect to. Let's say you want to find…

Q: Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the…

A: It is given that r1(t) and r2(t) are vector valued functions in 2-space. The objective is to explain…

Q: Let u = (3, 2, x) and v = (2x, 4, x). (a) Find all possible values of x that make u and v…

A: Given thata)We have to find all possible values of x that make u and v orthogonal.b)We have to find…

Q: Q3. a) Express the vector (4,2) e R' as linear combination of the vectors (1,1) and (1,-1). b) Let T…

A: We have to find all these

Q: Do only question 7

A: To find the equation of the plane that is tangent to the given surface at a specific point, we need…

Q: Find the cross product a * b. a=(4, 5, 0), b = (1, 0, 7) Verify that it is orthogonal to both a and…

A:

Q: Let x 4 || - N and y = Find the vector v = 3x - 4y and its additive inverse. 18 [2] 4

A: The additive inverse of a vector v = <a , b> is  - v = <-a , -b>

Q: 3. Check whether (2, 4) and (1, 2) are linearly dependent or not?

A: Linearly department vectors

Q: 5- Suppose that A = {x1 = (3,1,2), x2 = (0,0,2), x3 = (2,0,1)} then [A] = R³, that means for every…

A:

Q: Jacobian of the transformation. x = 8v + 8w2, y = 5w + 5u2, z = 3u + 3v z) II

A: We have to solve the given problem

Q: Do only question 8

A: To find the equation of the plane tangent to the surface  f(x,y)=x+yx​ at the point (1, 2), we need…

Q: Find the length of the projection of [−8 −7]onto the vector [−7 5]   Its written vertically…

A:

Q: Do only question 4

A: Questio(4)Part(a)Find limt→∞​r(t):Given r(t)=⟨2sin(t),3cos(t),t2⟩, as t→∞,sin(t) and cos(t)…

Q: Show that u1 =(2,1,1) u2= (-2,2,1) u3= (1,-1,-2) are linearly dependent show all working and explain…

A: Given :u1 =(2,1,1) u2= (-2,2,1) u3= (1,-1,-2)

Q: Match each vector field with its graph. xi + yj + zk (x² + y² +2²)3/2 C# 27= = 3.7 = x² + yj D#…

A: According to the given data, match each vector field with its graph.

Q: Do question 9 only

A: Step 1: Compute the Gradient of 𝑓Given f(x,y)=x2ey,Compute the partial…

Q: Let A = -2 10] -2 40-0 12 b= -1 -3 1 1 6 and c = -27 -3

A:

Q: If a, and b are non - collinear vector and vectors a = (x +4 y)a +(2x + y +1)b and, B= (-2x + y + 2…

A: We will solve the following

Q: 2. Consider the vectors =(1,2,3,0),= (0,1,2,3) and = (2,3,4,-3) Let = (1,1,1,1) (a) Is a linear…

A:

Q: 1. Given vectors B = (1,–2,3,0),C =(-2,1,0,4) in R*. (a) Examine if vector X = (-4,-1,6,12) is in…

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Q: Mickey Mantle played for the New York Yankees for 18 years from 1951 to 1968. Year by year he hit…

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