ACT Math · Matrices and vectors

What is bmatrix 7 & 2 \\ 5 & 9 bmatrix - bmatrix 3 & 4 \\ 1 & 6 bmatrix?

What is [7259]−[3416]\begin{bmatrix} 7 & 2 \\ 5 & 9 \end{bmatrix} - \begin{bmatrix} 3 & 4 \\ 1 & 6 \end{bmatrix}?

Answer and explanation

Answer: F: bmatrix 4 & -2 \\ 4 & 3 bmatrix

Subtract corresponding entries: 7−3=47-3=4, 2−4=−22-4=-2, 5−1=45-1=4, and 9−6=39-6=3, giving [4−243]\begin{bmatrix}4&-2\\4&3\end{bmatrix}, choice F. Choice G has 22 in place of −2-2, which comes from computing 4−24-2 rather than 2−42-4 in the top-right position. Choice H adds the matrices instead of subtracting them. Choice J is B−AB-A, with every sign reversed, so the order of subtraction is wrong. Matrix subtraction is not commutative, so the first matrix always comes first and the second is subtracted from it.

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