Find the matrix of the linear transformation T: V ? W relative to B and C. Suppose B = {b1, b2, b3} is a basis for V and C = {c1, c2} is a basis for W. Let T be defined by T(b1) = 3c1 + c2 T(b2) = 8c1 - 8c2 T(b3) = 3c1 + 2c2 [ 3 4 8 0 3 5 ] [ 4 0 5 1 -8 2 ] [ 3 8 3 1 -8 2 ] [ 3 1 8 -8 3 2 ]
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To do this, we will express the images of the basis vectors of B under T in terms of the basis vectors of C. We are given that: T(b1) = 3c1 T(b2) = 8c1 + 8c2 T(b3) = 3c1 + 2c2 Now, we will express these images as column vectors in terms of the basis C: T(b1) = Show more…
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