If A = [ 2 - 3 0 2 5 1 1 3 ] , then A - 1 exists if:

Question

If $A = [\begin{matrix} 2 & λ & - 3 \\ 0 & 2 & 5 \\ 1 & 1 & 3 \end{matrix}],$ then $A^{- 1}$ exists if:

Smart Achievers · Accepted Answer

(4)

Ans. None of these

Explanation:

We have, $A = [\begin{matrix} 2 & λ & - 3 \\ 0 & 2 & 5 \\ 1 & 1 & 3 \end{matrix}]$

$A^{- 1}$ exists if $| A |$ $\neq 0$

Now, $| A |$ $= 2 (6 - 5) - λ (- 5) - 3 (- 2) = 8 + 5 λ$

But, $| A |$ $\neq 0$

$5 λ + 8 \neq 0$ $\Rightarrow 5 λ \neq - 8$

$\Rightarrow$ $λ \neq - \frac{8}{5}$

So, $A^{- 1}$ exists if and only if $λ \neq \frac{- 8}{5}$

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