A row operation is performed on a matrix as shown. the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 1 column 3, 1 column 4, 4 row 2, column 1, 1 column 2, 1 column 3, 1 column 4, 11 row 3, column 1, 4 column 2, negative 2 column 3, 2 column 4, 5 ce bond right arrow the 3 by 4 matrix, row 1, column 1, 0 column 2, negative 3 column 3, x column 4, negative 18 row 2, column 1, 1 column 2, 1 column 3, 1 column 4, 11 row 3, column 1, 4 column 2, negative 2 column 3, 2 column 4, 5 What is the value of x ?
The first row changes from (2, −1, 1, 4) to (0, −3, x, −18), while the other rows stay the same. This matches the row operation R₁ → R₁ − 2R₂: for the third entry, x = 1 − 2(1) = −1. So the correct choice is negative 1.
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