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Multiplication of Matrices

Find the outp...

Question

Find the output order for the following matrix multiplication $X_{5 \times 3} \times Y_{3 \times 5}$ ?

5 \times 5

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3 \times 5

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5 \times 3

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3 \times 3

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Solution

The correct option is A $5 \times 5$
Since, $X$ is of size $5 \times 3$ , and $Y$ is of size $3 \times 5$
$∴$ The matrix product of $X$ and $Y$ has order $5 \times 5.$

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(- 5) \times 3 = 3 \times (- 5) = (- 15)

A = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{3} \frac{1}{3} \frac{7}{3} \end{matrix} \begin{matrix} 1 \frac{2}{3} 2 \end{matrix} \begin{matrix} \frac{5}{3} \frac{4}{3} \frac{2}{3} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

B = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{5} \frac{1}{5} \frac{7}{5} \end{matrix} \begin{matrix} \frac{3}{5} \frac{2}{5} \frac{6}{5} \end{matrix} \begin{matrix} 1 \frac{4}{5} \frac{2}{5} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

3 A - 5 B

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