Suppose that vectors v1 = (1, 2), v2 = (2,−1), and that the basis B is B=v1, v2 . (this is a list) Let T be the linear transformation from R2 to R2 given by T(v1) = v1 and T(v2) = 0. (a) Write down the matrix for T in the new basis B. (You should be able to do this directly from the definition of T). (b) Use this to write down the matrix for T in the standard basis.

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Suppose that vectors v1 = (1, 2), v2 = (2,−1), and that the basis B is B=v1, v2 . (this is a list) Let T be the linear transformation from R2 to R2 given by T(v1) = v1 and T(v2) = 0. (a) Write down the matrix for T in the new basis B. (You should be able to do this directly from the definition of T). (b) Use this to write down the matrix for T in the standard basis.

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\[\vec{x}=\binom{x_1}{x_2};\ B=\{v_1,v_2\}\] \[[\vec{x}]_B=x_1v_1+x_2v_2\] \[\begin{align} T([\vec{x}]_B)&=T(x_1v_1+x_2v_2)\\\\ &=T(x_1v_1)+T(x_2v_2)\\\\ &=x_1T(v_1)+x_2T(v_2)\\ \end{align}\] \[T_B=\{T(v_1),T(v_2)\}\] \[T_e=\{T(e_1),T(e_2)\}\] and that is the best that I can come up with :)

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