If A - - 2 1- 0 3 - B - - 1 2- 3 -2 - whether AB is singular or non-singular-

A=[ 2 amp; 1; 0 amp; 3 ] B=[ 1 amp; 2; 3 amp; 2 ] AB=[ 2 amp; 1; 0 amp; 3 ][ 1 amp; 2; 3 amp; 2 ] ...

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Standard XII

Mathematics

Elementary Transformations

If A = [ 2 ...

Question

If $A = [\begin{matrix} 2 & 1 0 & 3 \end{matrix}] B = [\begin{matrix} 1 & 2 3 & - 2 \end{matrix}]$ whether $A B$ is singular or non-singular.

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Solution

$A = [\begin{matrix} 2 & 1 0 & 3 \end{matrix}] B = [\begin{matrix} 1 & 2 3 & - 2 \end{matrix}] A B = [\begin{matrix} 2 & 1 0 & 3 \end{matrix}] [\begin{matrix} 1 & 2 3 & - 2 \end{matrix}] A B = [\begin{matrix} 5 & 2 9 & - 6 \end{matrix}] | A B | = - 30 - 18 = - 48 \neq 0$
$∴$ AB is a non-singular matrix.

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If A=[2103]B=[123−2] whether AB is singular or non-singular.

A=[2103]B=[123−2]AB=[2103][123−2]AB=[529−6]|AB|=−30−18=−48≠0∴ AB is a non-singular matrix.

If $A = [\begin{matrix} 2 & 1 0 & 3 \end{matrix}] B = [\begin{matrix} 1 & 2 3 & - 2 \end{matrix}]$ whether $A B$ is singular or non-singular.