Question

If A = `[(1,2,3), (2,k,2), (5,7,3)]` is a singular matrix then find the value of 'k'.

Answer 1

A = `[(1,2,3), (2,k,2), (5,7,3)]`

As A is a singular matrix.
|A| = o

`|(1,2,3), (2,k,2), (5,7,3)|` = o

1(3k - 14) - 2(6 - 10) + 3(14 - 5k) = 0
3k - 14 + 8 + 42 - 15k = o
`therefore` -12k + 36 = 0
`therefore` -12k = -36
`therefore k = (-36)/(-12)`
k = 3