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Multiplication of Matrices

Find AB when ...

Question

$Find A B when A = [\begin{matrix} 1 & 0 4 & 1 \end{matrix}] and B = [\begin{matrix} - 1 & 0 - 4 & - 1 \end{matrix}] .$

A

[\begin{matrix} - 1 & 0 - 8 & - 1 \end{matrix}]

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B

[\begin{matrix} 1 & 0 8 & 1 \end{matrix}]

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C

[\begin{matrix} - 1 & - 8 0 & - 1 \end{matrix}]

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D

[\begin{matrix} 0 & - 1 - 8 & 0 \end{matrix}]

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Solution

The correct option is A $[\begin{matrix} - 1 & 0 - 8 & - 1 \end{matrix}]$
$A = [\begin{matrix} 1 & 0 4 & 1 \end{matrix}], B = [\begin{matrix} - 1 & 0 - 4 & - 1 \end{matrix}]$
$A B = [\begin{matrix} 1 \times (- 1) + 0 \times (- 4) & 1 \times 0 + 0 \times (- 1) 4 \times (- 1) + 1 \times (- 4) & 4 \times 0 + 1 \times (- 1) \end{matrix}]$
$= [\begin{matrix} - 1 & 0 - 8 & - 1 \end{matrix}]$

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A + 3 B + 4 I .

Q. If a, b, c, d denote the determinants of matrices A, B, C, D where
A=

⎡ ⎢ ⎣ \begin{matrix} 0 & x - y & x - z y - x & 0 & y - z z - x & z - y & 0 \end{matrix} ⎤ ⎥ ⎦

⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 2 & 3 & 4 4 & 9 & 16 \end{matrix} ⎤ ⎥ ⎦

⎡ ⎢ ⎣ \begin{matrix} 0 & 0 & 2 0 & 5 & 0 7 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦

⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 1 & 2 & 8 1 & 3 & 27 \end{matrix} ⎤ ⎥ ⎦

Then the ascending order of a, b, c, d

A = [\begin{matrix} 2 & 4 & - 1 - 1 & 0 & 2 \end{matrix}], B = ⎡ ⎢ ⎣ \begin{matrix} 3 & 4 - 1 & 2 2 & 1 \end{matrix} ⎤ ⎥ ⎦

(A B)^{T}

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If A = $[\begin{matrix} 3 & 7 2 & 4 \end{matrix}], B = [\begin{matrix} 0 & 2 5 & 3 \end{matrix}]$ , and $C = [\begin{matrix} 1 & - 5 - 4 & 6 \end{matrix}]$ , find AB - 5C.

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