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1. Determine whether each of the following is a linear transformation. a. L: R3 → R2 defined by L(x,y, z) = (Ix), y + z) b. L: M2x2 → P3 defined by L ( 2) = ax + (a + b)x? + (c + d)x +c C. L: R2 → R3 defined by L(x,y) = (x +1, 2y, x+ y)

1. Determine whether each of the following is a linear transformation. a. L: R3 → R2 defined by L(x,y, z) = (Ix), y + z) b. L: M2x2 → P3 defined by L ( 2) = ax + (a + b)x? + (c + d)x +c C. L: R2 → R3 defined by L(x,y) = (x +1, 2y, x+ y)

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 16CM
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1. Determine whether each of the following is a linear transformation. a. L: R3 → R2 defined by L(x,y,z) = (\x), y + z) b. L: M2x2 → P3 defined by L ( 2) = ax + (a + b)x? + (c + d)x+c C. L: R² → R³ defined by L(x,y) = (x + 1, 2y, x + y)
Transcribed Image Text:1. Determine whether each of the following is a linear transformation. a. L: R3 → R2 defined by L(x,y,z) = (\x), y + z) b. L: M2x2 → P3 defined by L ( 2) = ax + (a + b)x? + (c + d)x+c C. L: R² → R³ defined by L(x,y) = (x + 1, 2y, x + y)
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