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Find K if the following matrices are singular. K[K-1233121-24] - Mathematics and Statistics

Sum

Find K if the following matrices are singular.

`[("K"-1, 2, 3),(3, 1, 2),(1, -2, 4)]`

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Solution

Let A = `[("K"-1, 2, 3),(3, 1, 2),(1, -2, 4)]`

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

∴ `|("K"-1, 2, 3),(3, 1, 2),(1, -2, 4)|` = 0

∴ (K – 1)(4 + 4) –2(12 –2) + 3(–6 – 1) = 0
∴ 8K – 8 – 20 – 21 = 0
∴ 8K  = 49
∴ K = `(49)/(8)`.

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