Q33 of 58 Page 77

If , then A-1 exists if

Given


⇒ |A| = 2 (6 – 5) - λ (0 – 5) + (-3) (0 – 2)


= 2 + 5λ + 6


= 5λ + 8


We know that A-1 exists if A is non – singular matrix i.e. |A| ≠ 0.


∴ 5λ + 8 ≠ 0


⇒ 5λ ≠ -8



So, A-1 exists if and only if .

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