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