Question

If a=[{2,lamda,-3},{0,2,5},{1,1,3}] then a^-1 exist find the value of lamda

Answer 1

your question is ---> if $a=\begin{vmatrix}2 & \lambda & 3\\0 & 2 & 5\\1 & 1 & 3\end{vmatrix}$ then a^-1 exist find value of λ.

(A) λ = 2

(B)λ ≠ 2

(C)λ ≠ -2

(D) none of these.

from concept of inverse of matrix

we know, inverse of any matrix a is possible only when a is non - singular matrix.

i.e., |a| ≠ 0

so, determinant of a , |a| = 2(2 × 3 - 5 × 1) - λ(0 × 3 - 1 × 5) + (-3) (1 × 0 - 1 × 2) ≠ 0

or, 2(6 - 5) + 5λ + 6 ≠ 0

or, 5λ + 8 ≠ 0

or, λ ≠ -8/5

hence value of λ is all real numbers except x = -8/5 .

so, option (A) is correct choice.