Answered: Find T(v) by using the matrix relative…

Find T(v) by using the matrix relative to B and B'. T: R2 → R3, T(x, y) = (x + y, x, y), v = (7, 4), B = {(1, −1), (0, 1)},B' ={(1, 1, 0),(0, 1, 1),(1, 0, 1)}

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Let A = MB (f) be the matrix associated with the linear map f((x,y,z)=(x − 2y,y+z,0) relative to the bases B={u= (1,0,3); v = (0,2,1); w=(2, 1,0) } and B'={u'=(0,0,2) ;v' = (1,0, 3) ;w '= (1,2,1) }. Then the third column of A is: A. (-1/2 1/2 1/2 B. OC. 1/2 - 1/2 1/2 1/2 1/2 - 1/2 D. °°) E. 2 of (3)
2. Write the quadratic function f (x,,y,)=-3x; +2x,x, – 3x; – 4x, – 4x, +6 in matrix form as f(x) = x'Ax + b'x + c and hence find af dx
Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4, 4)} be bases for R², and let 23 = [33] 04 A = R2 relative to B. (a) Find the transition matrix P from B' to B. be the matrix for T: R² ->>> P = 6 9 [V] B [T(V)]B = (b) Use the matrices P and A to find [v] and [T(v)]B, where [V] B¹ = [-4 3]. -12 -1/3 -24 -96 4 -96 4 11 ← (c) Find P-1 and A' (the matrix for T relative to B'). 1/3
Show that w is in span(B). We want to solve B - (-)-~-] = W = -1 Thus C₁ = 048 2 + C₂ so set up the augmented matrix of the linear system and row-reduce to solve it: [w] B = 12 1 1 0 0 -1 and C₂ = 00 8 [3]. + Find the coordinate vector [w]B. 3 R₂-2R₁ -=1/R₂2 R₁ - R₂ R₂ + R₂ 1 1 0-2 0 -1 1 0 1 0 -1 1 0 0 1 0 0 so that
Consider the following. B = {(0, -1, -2), (4, 1, 2), (12, 3, 7)}, B' = {(-3, -2, -6), (2, 1, 3), (2, 1, 4)}, 1 [x] B' = 2 -1 (a) Find the transition matrix from B to B'. p-1 = (b) Find the transition matrix from B' to B. P = (c) Verify that the two transition matrices are inverses of each other. PP-1 =
Good evening please assist with calculation.
Write the system in matrix form x' = 3x – 4y + z +t, y' = x + 2y – z + t?, z' = 6y – 7z + t³
Let f(u, v) = (u - v, 1, u + v) and g(x, y, z) = xyz. Find the entry a12 (i.e. the entry in the first row and second column) of the derivative matrices Df(u, v), Dg(x, y, z) and D(gof)(0, 1). (a) a 12 of Df(u, v) is (b) a12 of Dg(x, y, z) is (c) a12 of D(gof)(0, 1) is (d) Select the correct answer about D(g. f)(u, v) D(gof)(u, v) is a 1 x 2 matrix. D(gof)(u, v) is a 2 x 2 matrix. D(gof)(u, v) is a 3 x 2 matrix. D(gof)(u, v) is a 2 x 3 matrix. D(gof)(u, v) is a real-valued function of u and v. (e) Select the correct answer about D(f g)(x, y, z) OD(fog)(x, y, z) is not defined. D(fog)(x, y, z) is a real-valued function of x and y. D(fog)(x, y, z) is a 3 x 2 matrix. D(fog)(x, y, z) is a 2 x 2 matrix. D(fog)(x, y, z) is a 2 x 1 matrix.
Let f(u, v) = (u - v, 1,u + v) and g(x, y, z) = xyz. Find the entry a12(i.e. the entry in the first row and second column) of the derivative matrices Df(u, v), Dg(x, y) and D(g. f)(0, 1). (a) a12 of Df(u, v) is (b) a12 of Dg(x, y, z) is (c) a12 of D(g)(0, 1) is (d) Select the correct answer about D(g. f)(u, v) OD(g. f)(u, v) is a real-valued function of u and v. D(g. f)(u, v) is a 2 x 2 matrix. D(g. f)(u, v) is a 2 x 3 matrix. D(g f)(u, v) is a 3 x 2 matrix. 0 D(g f)(u, v) is a 1 x 2 matrix. (e) Select the correct answer about D(f g)(x, y, z) OD(fog)(x, y, z) is a real-valued function of x and y. D(fog)(x, y, z) is a 2 x 1 matrix. D(f g)(x, y, z) is not defined. 0 D(f g)(x, y, z) is a 3 x 2 matrix. D(f g)(x, y, z) is a 2 x 2 matrix.
Find the standard matrices A and A' for T = T₂ o T₁ and T' = T₁ 0 T₂. T₁: R² → R², T₁(x, y) = (x - 5y, 2x + 3y) T₂: R² R², T₂(x, y) = (0, x) A = Juma A' = SHE