A First Course in Linear Algebra · Problem MR.C30

Representations — Robert Beezer

Mathematics — Linear Algebra · kernel-range-matrix-representation

Problem

Find bases for the kernel and range of the linear transformation SS below. S:M22→P2,S([abcd])=(a+2b+5c−4d)+(3a−b+8c+2d)x+(a+b+4c−2d)x2S: M_{22} \to P_2, \quad S\left(\begin{bmatrix}a&b\\c&d\end{bmatrix}\right) = (a+2b+5c-4d)+(3a-b+8c+2d)x+(a+b+4c-2d)x^2

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