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Let $A_{t} = (\begin{array}{ccc} 1 & 3 & 2 \\ 2 & 5 & t \\ 4 & 7 - t & - 6 \end{array})$ then the value(s) of t for which inverse of $A_{t}$ does not exist.

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detailed solution

Correct option is C

Since At –1 does not exist, | At | = 0 ⇒(−30−t(7−t))−3(−12−4t)+2(14−2t−20)=0⇒t2+t−6=0⇒t=−3,2

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Let At=13225t47−t−6 then the value(s) of t for which inverse of At does not exist.

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Let $A_{t} = (\begin{array}{ccc} 1 & 3 & 2 \\ 2 & 5 & t \\ 4 & 7 - t & - 6 \end{array})$ then the value(s) of t for which inverse of $A_{t}$ does not exist.