The matrix represents a system of equations. the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 1 column 3, negative 3 column 4, negative 20 row 2, column 1, negative 2 column 2, negative 6 column 3, 6 column 4, negative 4 row 3, column 1, 0 column 2, 3 column 3, negative 2 column 4, negative 9 Which matrix represents 1 half cap r 2 plus cap r 3 rightarrow cap r 3 ? A
the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 1 column 3, negative 3 column 4, negative 20 row 2, column 1, negative 1 column 2, negative 3 column 3, 3 column 4, negative 2 row 3, column 1, 0 column 2, 6 column 3, negative 4 column 4, negative 18 B
the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 1 column 3, negative 3 column 4, negative 20 row 2, column 1, negative 2 column 2, negative 6 column 3, 6 column 4, negative 4 row 3, column 1, negative 1 column 2, 0 column 3, 1 column 4, negative 11 C
the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 1 column 3, negative 3 column 4, negative 20 row 2, column 1, negative 2 column 2, negative 6 column 3, 6 column 4, negative 4 row 3, column 1, negative 2 column 2, negative 3 column 3, 4 column 4, negative 13 D
the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 1 column 3, negative 3 column 4, negative 20 row 2, column 1, negative 1 column 2, negative 3 column 3, 3 column 4, negative 2 row 3, column 1, 0 column 2, 3 column 3, negative 2 column 4, negative 9 First multiply row 2, (−2, −6, 6, −4), by 1/2 to get (−1, −3, 3, −2). Add that to row 3, (0, 3, −2, −9), to replace row 3 with (−1, 0, 1, −11). The other rows stay unchanged, so the correct choice is A, the matrix with that new third row.
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