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Question
Identify the following matrix is singular or non-singular?
`[("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")]`
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Solution
Let A = `[("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")]`
∴ | A | = `|("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")|`
= `|("a", "b", "c"),("p", "q", "r"),(2"a", 2"b", 2"c")| + |("a", "b", "c"),("p", "q", "r"),(-"p", -"q", -"r")|`
By taking 2 and – 1 common from R3 in the first and second determinants respectively, we get,
| A | = `2|("a", "b", "c"),("p", "q", "r"),("a", "b", "c")| - |("a", "b", "c"),("p", "q", "r"),("p", "q", "r")|`
= 2 x 0 – 0
= 0
∴ A is a singular matrix.
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