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1. Assume thatT is a linear transformation. Find the standard matrix of T. (a) T: R → R* with T(e1) = (2, -1,3, 7) and T(e2) = (5,0, -2, 1). (b) T: R² → R² that first reflects points across the vertical rz axis and then rotates points radians counterclockwise. 2. Let T(r1, 12, 13) = (x1 – 5x2 + 4r3, T2 – 6r3). (a) Show that T is a linear transformation by finding a matrix that implements the mapping. (b) Is T one-to-one? (c) Does T map R onto R??

1. Assume thatT is a linear transformation. Find the standard matrix of T. (a) T: R → R* with T(e1) = (2, -1,3, 7) and T(e2) = (5,0, -2, 1). (b) T: R² → R² that first reflects points across the vertical rz axis and then rotates points radians counterclockwise. 2. Let T(r1, 12, 13) = (x1 – 5x2 + 4r3, T2 – 6r3). (a) Show that T is a linear transformation by finding a matrix that implements the mapping. (b) Is T one-to-one? (c) Does T map R onto R??

Advanced Engineering Mathematics
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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Section 1.9 1. Assume that T is a linear transformation. Find the standard matrix of T. (a) T: R? → R' with T(e1) = (2, -1,3, 7) and T(e2) = (5,0, -2, 1). (b) T : R? → R² that first reflects points across the vertical r2 axis and then rotates points * radians counterclockwise. 2. Let T(x1, #2, x3) = (x1 - 5a2 + 4.x3, *2 – 6x3). (a) Show that T is a linear transformation by finding a matrix that implements the mapping. (b) Is T one-to-one? (c) Does T map R³ onto R'?
Transcribed Image Text:Section 1.9 1. Assume that T is a linear transformation. Find the standard matrix of T. (a) T: R? → R' with T(e1) = (2, -1,3, 7) and T(e2) = (5,0, -2, 1). (b) T : R? → R² that first reflects points across the vertical r2 axis and then rotates points * radians counterclockwise. 2. Let T(x1, #2, x3) = (x1 - 5a2 + 4.x3, *2 – 6x3). (a) Show that T is a linear transformation by finding a matrix that implements the mapping. (b) Is T one-to-one? (c) Does T map R³ onto R'?
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