The matrix represents a system of equations. the 3 by 4 matrix, row 1, column 1, 2 column 2, 1 column 3, 1 column 4, 4 row 2, column 1, negative 3 column 2, 2 column 3, negative 1 column 4, negative 8 row 3, column 1, 1 column 2, negative 1 column 3, 1 column 4, 5 Which matrix represents the solution to this system of equations? A
the 3 by 4 matrix, row 1, column 1, 1 column 2, 0 column 3, 0 column 4, 2 row 2, column 1, 0 column 2, 1 column 3, 0 column 4, negative 4 row 3, column 1, 0 column 2, 0 column 3, 1 column 4, 3 B
the 3 by 4 matrix, row 1, column 1, 2 column 2, 1 column 3, 1 column 4, 4 row 2, column 1, negative 3 column 2, 2 column 3, negative 1 column 4, negative 8 row 3, column 1, 1 column 2, negative 1 column 3, 1 column 4, 5 C
the 3 by 4 matrix, row 1, column 1, 1 column 2, 0 column 3, 0 column 4, 1 row 2, column 1, 0 column 2, 1 column 3, 0 column 4, negative 1 row 3, column 1, 0 column 2, 0 column 3, 1 column 4, 3 D
the 3 by 4 matrix, row 1, column 1, 1 column 2, 0 column 3, 0 column 4, 4 row 2, column 1, 0 column 2, 1 column 3, 0 column 4, negative 8 row 3, column 1, 0 column 2, 0 column 3, 1 column 4, 5 The rows represent the equations 2x + y + z = 4, −3x + 2y − z = −8, and x − y + z = 5. Solving them gives x = 1, y = −1, and z = 3, so the equivalent solution matrix has the identity matrix on the left and 1, −1, 3 in the final column. That is choice C.
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