(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
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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.
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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