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Question: If for AX = B, B = \(\begin{bmatrix} 9 \\ 52 \\ 0 \end{bmatrix}\) and A<sup>–1</sup> = \(\begin{bma...

If for AX = B, B = [9520]\begin{bmatrix} 9 \\ 52 \\ 0 \end{bmatrix} and

A–1 = [3–1/2–1/2–43/45/42–1/4–3/4]\begin{bmatrix} 3 & –1/2 & –1/2 \\ –4 & 3/4 & 5/4 \\ 2 & –1/4 & –3/4 \end{bmatrix}then X is equal to –

A

[33/4–3/4]\begin{bmatrix} 3 \\ 3/4 \\ –3/4 \end{bmatrix}

B

[–1/2–1/22]\begin{bmatrix} –1/2 \\ –1/2 \\ 2 \end{bmatrix}

C

[–423]\begin{bmatrix} –4 \\ 2 \\ 3 \end{bmatrix}

D

[135]\begin{bmatrix} 1 \\ 3 \\ 5 \end{bmatrix}

Answer

[135]\begin{bmatrix} 1 \\ 3 \\ 5 \end{bmatrix}

Explanation

Solution

X = A–1B

X =[3−1/2−1/2−43/45/42−1/4−3/4]\left[ \begin{array} { c c c } 3 & - 1 / 2 & - 1 / 2 \\ - 4 & 3 / 4 & 5 / 4 \\ 2 & - 1 / 4 & - 3 / 4 \end{array} \right] [9520]\begin{bmatrix} 9 \\ 52 \\ 0 \end{bmatrix}̃ X = [135]\begin{bmatrix} 1 \\ 3 \\ 5 \end{bmatrix}