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  • State True or False for the statements If A and B are matrices of order 3 and |A| = 5, |B| = 3, then |3AB| = 27 × 5 × 3 = 405.

State True or False for the statements

If A and B are matrices of order 3 and |A| = 5, |B| = 3, then |3AB| = 27 × 5 × 3 = 405.

 

Answers (1)

We know that:
\\ \vspace{\baselineskip} $ \vert $ AB$ \vert $ = $ \vert $ A$ \vert $ . $ \vert $ B$ \vert $ and if A = [a\textsubscript{ij}]\textsubscript{3$ \times $ 3}, then $ \vert $ k.A$ \vert $ = k\textsuperscript{3}$ \vert $ A$ \vert $ .

\\ \\ \\ \vspace{\baselineskip}$ \therefore $ $ \vert $ 3A$ \vert $ = 27 $ \vert $ AB$ \vert $ \\ \\ \vspace{\baselineskip}= 27 $ \vert $ A$ \vert $ $ \vert $ B$ \vert $ \\ \\ \vspace{\baselineskip}= 27 (5) (3)\\ \\ \vspace{\baselineskip}= 405\\ \vspace{\baselineskip}

Hence the statement given in question is true.

Posted by

infoexpert22

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