If the matrix [ * 20 c 1&3& + 2 2&4&8 3&5& 10 ] is singular, then… - Vidyadip

Question

If the matrix $\left[ {\begin{array}{*{20}{c}}1&3&{\lambda + 2}\\2&4&8\\3&5&{10}\end{array}} \right]$ is singular, then $\lambda = $

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Answer

b
(b) The matrix $\left[ {\begin{array}{*{20}{c}}1&3&{\lambda + 2}\\2&4&8\\3&5&{10}\end{array}} \right]$ is singular,

If $\,\left| {\,\begin{array}{*{20}{c}}1&3&{\lambda + 2}\\2&4&8\\3&5&{10}\end{array}\,} \right| = 0$

==> $1(40 - 40) - 3(20 - 24) + (\lambda + 2)(10 - 12) = 0$

==> $2(\lambda + 2) = 12 \Rightarrow \lambda = 4.$

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