(1) Which of the following linear transformations is 1-1? (a) T(1,y) = (x + y,r+y) (b) T(r,y) =2r + 3y (c) T(z,y, 2) = (2r - 3y, r-4y) (d) T(1,y, 2) = (-y, 3z, 82) (e) T(1,y, 2) = (z + y,y+,1 + 2y + 2) %3D

Elementary Linear Algebra (MindTap Course List)
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Author:Ron Larson
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Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...
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(1)
Which of the following lincear transformations is 1-1?
(a) T(1,y) = (x + y,z+y)
(b) T(1, y) = 2r + 3y
(c) T(1,y, =) = (2r- 3y, r-4y)
(d) T(1,y, 2) = (-y,3z, 82)
(e) T(1,y, 2) = (z + y,y+ ,1 + 2y + 2)
%3D
(2)
Which one of the following matrices is invertible?
3 -6
(c)
-3
(a)
1 0-1
(e)
-1
-1
2 3
-2
-1
41-3
(b) o o
0 0
0 0 0
(d)
100
0 5 0
Transcribed Image Text:(1) Which of the following lincear transformations is 1-1? (a) T(1,y) = (x + y,z+y) (b) T(1, y) = 2r + 3y (c) T(1,y, =) = (2r- 3y, r-4y) (d) T(1,y, 2) = (-y,3z, 82) (e) T(1,y, 2) = (z + y,y+ ,1 + 2y + 2) %3D (2) Which one of the following matrices is invertible? 3 -6 (c) -3 (a) 1 0-1 (e) -1 -1 2 3 -2 -1 41-3 (b) o o 0 0 0 0 0 (d) 100 0 5 0
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