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  • Find the value of a for which <img alt="\\\mathrm{A = \begin{bmatrix} 1 &2 &3 \\ -1 &a &2 \\ 2& 4 & 6 \end{bmatrix}}" src="https://entrancecorner.oncodecogs.c

Find the value of a for which \\\mathrm{A = \begin{bmatrix} 1 &2 &3 \\ -1 &a &2 \\ 2& 4 & 6 \end{bmatrix}} is a singular matrix.

Option: 1

-1


Option: 2

0


Option: 3

1


Option: 4

All of the above


Answers (1)

best_answer

For singular matrix det A is 0.

\\\mathrm{|A| = \begin{vmatrix} 1 &2 &3 \\ -1 &a &2 \\ 2& 4 & 6 \end{vmatrix} = 1\cdot(6a-2\cdot 4) -2\cdot(-6-4)+3\cdot(-4-2a)} \\\mathrm{|A| = (6a-8) +20 -12-6a = 0}

Hence for all values of a matrix A is a singleton matrix.

Hence, option (d) is correct

Posted by

Gautam harsolia

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