Let B and C be two ordered bases of R^2, and consider a linear transformation T : R^2 ? R^2. Suppose that the change of base matrix I_{C,B} is given by [ -1 -2 ] [ -3 -1 ] and the coordinate matrix T_{C,C} of T with respect to C is given by [ 2 1 ] [ 2 -1 ]. Use this to determine coordinate matrix T_{B,B} of T with respect to B! T_{B,B} =
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We want to find the coordinate matrix of T with respect to B, which is $T_{B,B}$. We can use the following formula to find $T_{B,B}$: $$T_{B,B} = I_{C,B}^{-1} T_{C,C} I_{C,B}$$ Show more…
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