(b) Consider the ordered basis B = {fi, f2, f3. f} of R where 0-0-0 -0 fy and let S:R-→ R be the linear transformation defined by S(f.) = 4fi- 2, S(6) = -fj + 4f S(f,) = 6f, - 2f, and S(f1) =-2f, + 6f. () Write down the matrix A that represents S with respect to the ordered basis B. (ii) Use your matrix A to express the vectors 3+B S(f; + f,), S(f-f2), S(f, + f) and S(-f) as linear combinations of f,, f2, fy and f,.

(b) Consider the ordered basis B = {fi, f2, f3. f} of R where 0-0-0 -0 fy and let S:R-→ R be the linear transformation defined by S(f.) = 4fi- 2, S(6) = -fj + 4f S(f,) = 6f, - 2f, and S(f1) =-2f, + 6f. () Write down the matrix A that represents S with respect to the ordered basis B. (ii) Use your matrix A to express the vectors 3+B S(f; + f,), S(f-f2), S(f, + f) and S(-f) as linear combinations of f,, f2, fy and f,.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 11CM

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Question

Here is a simple question regarding Matrices attached. Please review it and I need the solution of it.

(b) Consider the ordered basis B = {fi, f2, f3. f} of R where
0-0-0 -0
fy
and let S:R-→ R be the linear transformation defined by
S(f.) = 4fi- 2, S(6) = -fj + 4f S(f,) = 6f, - 2f, and S(f1) =-2f, + 6f.
() Write down the matrix A
that represents S with respect to the ordered basis B.
(ii) Use your matrix A to express the vectors
3+B
S(f; + f,),
S(f-f2), S(f, + f)
and
S(-f)
as linear combinations of f,, f2, fy and f,.

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