A First Course in Linear Algebra · Problem MR.C50

Representations — Robert Beezer

Mathematics — Linear Algebra · range-matrix-representation

Problem

Use a matrix representation to find a basis for the range of the linear transformation LL. L:M22→P2,T([abcd])=(a+2b+4c+d)+(3a+c−2d)x+(−a+b+3c+3d)x2L: M_{22} \to P_2, \quad T\left(\begin{bmatrix}a&b\\c&d\end{bmatrix}\right) = (a+2b+4c+d)+(3a+c-2d)x+(-a+b+3c+3d)x^2

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