Let E= te, e, e be the standard basis for R', let B= (b, bz. b, be a basis for a vector space V. and let T:R'- V be a lincar transformation with the property that T(x.. Ka. Xa) = (2x, - x)b, – (2x5)b; + (x, + 3x, )b, a. Compute T(e,). T (e:), and T(e,). b. Compute (T(s, )ls. [T(s;)]g, and (T(s,)]s. e. Find the matrix for T relative to E and B. Let B = {b. b. b, be a basis for a vector space V and let T:V - R' be a lincar transformation with the property that 2x -3x +x T(x,b, + x,b; +x,b,) = -2x, + 5x, Find the matrix for T relative to B and the standard basis for R.
Let E= te, e, e be the standard basis for R', let B= (b, bz. b, be a basis for a vector space V. and let T:R'- V be a lincar transformation with the property that T(x.. Ka. Xa) = (2x, - x)b, – (2x5)b; + (x, + 3x, )b, a. Compute T(e,). T (e:), and T(e,). b. Compute (T(s, )ls. [T(s;)]g, and (T(s,)]s. e. Find the matrix for T relative to E and B. Let B = {b. b. b, be a basis for a vector space V and let T:V - R' be a lincar transformation with the property that 2x -3x +x T(x,b, + x,b; +x,b,) = -2x, + 5x, Find the matrix for T relative to B and the standard basis for R.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.1: Orthogonality In Rn
Problem 34EQ
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