(2) Consider the linear transformation in R.¹ given by T(a, b, c, d) = (a + 2b + 3d, c-a-2b-d, a + 2b+c+5d, a + 2b +2c +

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2 Consider The Linear Transformation In R Given By T A B C D A 2b 3d C A 2b D A 2b C 5d A 2b 2c 1 (67.65 KiB) Viewed 30 times

(2) Consider the linear transformation in R.¹ given by T(a, b, c, d) = (a + 2b + 3d, c-a-2b-d, a + 2b+c+5d, a + 2b +2c + 7d) (a) Write down the matrix representation of T with respect to the standard basis, that is, [T]. (b) Find ker T, writing your answer in the form (c) Show that ker T = span like we did in class. When row reducing matrices, please use indicate all row operations being used. B = {(1, 0, 0, 1), (0, 1, 0, 1), (0, 0,-1,-1), (1, 1, 1, 0)} is a basis of R¹ and compute the change of basis matrices [id] and [id]. When computing matrix inverses, please use Gaussian elimination indicating all row operations being used. (d) Use those change of basis matrices to compute [7].