If A = [(2,λ,-3)(0,2,5)(1,1,3)] then find the value of λ for which A^(–1) exists.

Question

If A = \(\begin{bmatrix} 2 & \lambda & -3 \\[0.3em] 0 & 2 & 5\\[0.3em] 1 & 1& 3 \end{bmatrix}\) then find the value of λ for which A^–1 exists.

Answer 1

For existence of A^-1

|A| ≠ 0  

⇒ \(\begin{bmatrix} 2 & \lambda & -3 \\[0.3em] 0 & 2 & 5\\[0.3em] 1 & 1& 3 \end{bmatrix}\)≠ 0

Hence, λ can have any value other than \(-\frac{8}{5}.\)