Question

For the matrix A = `[(2, -1, 1),(lambda, 2, 0),(1, -2, 3)]` to be invertible, the value of λ is ______.

विकल्प

• 0

• 10

• `RR - {10}`

• `RR - {-10}`

Answer 1

For the matrix A = `[(2, -1, 1),(lambda, 2, 0),(1, -2, 3)]` to be invertible, the value of λ is `underlinebb(RR - {-10})`.

Explanation:

A = `[(2, -1, 1),(lambda, 2, 0),(1, -2, 3)]`

For invertible, the Determinant of A should not be equal to zero.

`|A| = 2(6-0)-(-1)(3 lambda - 0) + 1 (-2 lambda - 2)`

`|A| = 12 + 3lambda - 2lambda - 2`

`|A| = 10 + lambda ≠ 0`

Therefore, λ ≠ −10