Question

Find K if the following matrices are singular.

`[(4, 3, 1),(7, "K", 1),(10, 9, 1)]`

Answer 1

Let A = `[(4, 3, 1),(7, "K", 1),(10, 9, 1)]`

Since A is a singular matrix,
|A| = 0

∴ `|(4, 3, 1),(7, "K", 1),(10, 9, 1)|` = 0

∴ 4(K – 9) – 3(7 – 10) + 1(63 – 10K) = 0

∴ 4K – 36 – 21 + 30 + 63 – 10K = 0

∴ – 6K + 36 = 0

∴ 6K = 36

∴ K = 6