Question

Find m if the matrix `[(1,1,3),(2,λ,4),(9,7,11)]` has no inverse.

Answer 1

Since, `[(1,1,3),(2,λ,4),(9,7,11)]` is no inverse, `[(1,1,3),(2,λ,4),(9,7,11)]` = 0

`1|(lambda, 4),(7,11)| -1 |(2,4),(9,11)| + 3|(2,lambda),(9,7)|` = 0

1[11λ – 28] – 1[22 – 36] + 3[14 – 9λ] = 0

11λ – 28 + 14 + 42 – 27λ = 0

- 16λ + 28 = 0

- 16λ = -28

λ = `(-28)/(-16) = 7/4`