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8. Prove that T: R³ R2 defined by T(x, y, z) = (x, 3y + 1) is not linear.

8. Prove that T: R³ R2 defined by T(x, y, z) = (x, 3y + 1) is not linear.

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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8. Prove that T: R³ → R2 defined by T(x, y, z) = (x, 3y + 1) is not linear. 9. Prove that T: R³ R³ defined by T(x, y, z) = (x, y, 0) is linear. Then find the standard matrix of the transformation. 10. Let T: R² R2 be a linear transformation that maps u = 4 . Find the matrix of this transformation. into and maps v = B into
Transcribed Image Text:8. Prove that T: R³ → R2 defined by T(x, y, z) = (x, 3y + 1) is not linear. 9. Prove that T: R³ R³ defined by T(x, y, z) = (x, y, 0) is linear. Then find the standard matrix of the transformation. 10. Let T: R² R2 be a linear transformation that maps u = 4 . Find the matrix of this transformation. into and maps v = B into
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