7. Suppose that T : R² → R² is linear, T(1,0) = (1, 4), andT(1, 1) = (2, 5). What is T(2, 3)? Is T one-to-one?

Answered: Image /qna-images/answer/e5ca4ea7-4418-4806-8ca5-492aafcf9b84.jpg

Answered: 7. Suppose that T : R² → R² is linear,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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dw If w(x,y,2) = xe and x=-4, y = 4-, z = -4 + 41. Find dt- (4 - 4:(4-t) le O A. -4| 1- -4 + 4t (-4 + 41) (4 - 1)_],"%.) -4 + 4" (-4 + 41) 1+ + OB. O C. No correct Answer 41 2 -4 + 4 (-4 + 41)² ] D (4-1) -41 1(4 -t) O E. -4| 3- -4 + 41 (-4 + 4t)
2. Let f(x,y)= 3x y. If C is the line segment from (1,1) to (2,3), evaluate Jef-r'dt.
4) Let f(x,y, z ) = . In(r+2y + 3z). Find Vf =
(i) Consider T: R³ R³ defined by T(T1, T2, T3) = (x₁, I₁+I₂, X₁ + x₂ + x3). If B = {₁, ₂, 3} and B' = {B₁, B2, B3}, where a₁ = (0, 1, 1), a₂ = (1,0,1), a3 = (1, 1,0), B₁ = (1,0,0), B₂ = (1,1,0), B3 = (1, 1, 1), what is the matrix [T]B-B?
6. Let f(x, y, z) = 3r?y + yz, where x = 3 – t2, y = 2t + t³, and VI+ 3t. Calculate when t = 1.
Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies. v(3,-2) = 0 Vs(3,-2) = 5 u(3,-2) = -3 Us(3,-2) = -7 ut(3,-2) = 7 Fu(-3,0) = -9 Vt(3,-2) = -1 Fv(-3,0) = -5 Find Wę(3,-2) and We(3,-2). Ws(3,-2) = W+(3,-2) =

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7. Suppose that T : R² → R² is linear, T(1,0) = (1, 4), and T(1, 1) = (2, 5). What is T(2, 3) ? Is T one-to-one?