(a) Assume T R2 R is a linear transformation with T(1,0) = 3 and T(0, 1) = -1. Calculate T(2,5). (b) Given that the linear transformation T: R³ → R² is defined by T(x, y, z) = (x, z), find ker T.
(a) Assume T R2 R is a linear transformation with T(1,0) = 3 and T(0, 1) = -1. Calculate T(2,5). (b) Given that the linear transformation T: R³ → R² is defined by T(x, y, z) = (x, z), find ker T.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 12EQ
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![(a) Assume T : R² → R is a linear transformation with T(1,0) = 3 and T(0, 1) = −1.
Calculate T(2,5).
(b) Given that the linear transformation T : R³ → R² is defined by T(x, y, z) = (x, z), find
ker T.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4ad3e1a-5eb7-4646-b724-5c75e9b9d297%2F75610999-098c-47a4-b1c1-d0edceaccc54%2Focx3ouhj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Assume T : R² → R is a linear transformation with T(1,0) = 3 and T(0, 1) = −1.
Calculate T(2,5).
(b) Given that the linear transformation T : R³ → R² is defined by T(x, y, z) = (x, z), find
ker T.
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