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Determinants

Question
CBSEENMA12034570
Wired Faculty App

For what values of x, is the following matrix singular?
open square brackets table row cell 3 minus 2 straight x end cell cell space space space space straight x plus 1 end cell row 2 cell space space space space 4 end cell end table close square brackets

Solution

Let straight A space equals space open square brackets table row cell 3 minus 2 straight x end cell cell space space straight x plus 1 end cell row 2 cell space space 4 end cell end table close square brackets
therefore space space space space space space space open vertical bar straight A close vertical bar space equals space open vertical bar table row cell 3 minus 2 straight x end cell cell space space space straight x plus 1 end cell row 2 cell space space space space space 4 end cell end table close vertical bar space equals space left parenthesis 3 minus 2 straight x right parenthesis thin space left parenthesis 4 right parenthesis space minus space left parenthesis straight x plus 1 right parenthesis thin space left parenthesis 2 right parenthesis space space space space space space space space space space space space space space space space space space space equals space 12 minus 8 straight x minus 2 straight x minus 2 space equals space 10 minus 10 space straight x straight A space will space be space singular space when space open vertical bar straight A close vertical bar space equals space 0 space straight i. straight e. space 10 minus 10 straight x space equals space 0 therefore space space space space space 10 space equals space 10 space space straight x space space space or space space space straight x space equals space 1.

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