Let V = R°. Let B = {(1,1, 1), (1, 2, 1), (–1, 1, 0)}. (a) Express (x, y, z) as a linear combination of vectors in B. (b) Use (a) to deduce that B is a basis of V. (C) Suppose that T : R³ → R² is a linear map so that T(1, 1, 1) = (2, 1), T(1, 2, 1) =(-1,3), T(-1,1,0) = (1, –1). Find T(r, y, z). (Hint: Use linearity and (a).)
Let V = R°. Let B = {(1,1, 1), (1, 2, 1), (–1, 1, 0)}. (a) Express (x, y, z) as a linear combination of vectors in B. (b) Use (a) to deduce that B is a basis of V. (C) Suppose that T : R³ → R² is a linear map so that T(1, 1, 1) = (2, 1), T(1, 2, 1) =(-1,3), T(-1,1,0) = (1, –1). Find T(r, y, z). (Hint: Use linearity and (a).)
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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