Let A = [ 1 - 2 3 1 2 1 2 - 3 ] . If A - 1 does not exist, then =

Question

Let $A = [\begin{matrix} 1 & - 2 & 3 \\ 1 & 2 & 1 \\ λ & 2 & - 3 \end{matrix}] .$ If $A^{- 1}$ does not exist, then $λ =$

Smart Achievers · Accepted Answer

(4)

Ans. $- 1$

Explanation:

Given,

$A = [\begin{matrix} 1 & - 2 & 3 \\ 1 & 2 & 1 \\ λ & 2 & - 3 \end{matrix}]$

Since $A^{- 1}$ does not exist $\Rightarrow$ $| A |$ $= 0$

Now, $1 (- 6 - 2) + 2 (- 3 - λ) + 3 (2 - 2 λ) = 0$

$- 8 - 6 - 2 λ + 6 - 6 λ = 0$

$- 8 λ - 8 = 0$

$λ = - 1$

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