Matrix cap c is a transformation of matrix cap b , and matrix cap b is a transformation of matrix cap A , as shown. cap A is equal to the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 2 column 3, 4 column 4, 6 row 2, column 1, 1 column 2, 3 column 3, 2 column 4, 4 row 3, column 1, 2 column 2, negative 1 column 3, 4 column 4, 6 1 half cap r 1 plus cap r 1 set over right arrow Matrix cap b negative cap r 1 plus cap r 2 rightarrow cap r 2 set over right arrow Matrix cap c Which matrix represents matrix cap c ?
First, replace row 1 with half of row 1: [2, −2, 4, 6] becomes [1, −1, 2, 3]. Then replace row 2 with row 2 minus the new row 1: [1, 3, 2, 4] − [1, −1, 2, 3] = [0, 4, 0, 1]. Row 3 stays unchanged, so matrix C is choice B.
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