1. is Singular Matrix ?
`[[1,1,1],[1,1,1],[1,1,1]]`Solution:A square matrix `A`, such that `|A| = 0`, is called a singular matrix.
| `A` | = | | `1` | `1` | `1` | | | `1` | `1` | `1` | | | `1` | `1` | `1` | |
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| `|A|` | = | | `1` | `1` | `1` | | | `1` | `1` | `1` | | | `1` | `1` | `1` | |
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`=1 xx (1 × 1 - 1 × 1) -1 xx (1 × 1 - 1 × 1) +1 xx (1 × 1 - 1 × 1)`
`=1 xx (1 -1) -1 xx (1 -1) +1 xx (1 -1)`
`=1 xx (0) -1 xx (0) +1 xx (0)`
`= 0 +0 +0`
`=0`
Here, `|A| = 0`, so `A` is a singular matrix
2. is Singular Matrix ?
`[[2,1,1],[1,2,1],[1,1,1]]`Solution:A square matrix `A`, such that `|A| = 0`, is called a singular matrix.
| `A` | = | | `2` | `1` | `1` | | | `1` | `2` | `1` | | | `1` | `1` | `1` | |
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| `|A|` | = | | `2` | `1` | `1` | | | `1` | `2` | `1` | | | `1` | `1` | `1` | |
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`=2 xx (2 × 1 - 1 × 1) -1 xx (1 × 1 - 1 × 1) +1 xx (1 × 1 - 2 × 1)`
`=2 xx (2 -1) -1 xx (1 -1) +1 xx (1 -2)`
`=2 xx (1) -1 xx (0) +1 xx (-1)`
`= 2 +0 -1`
`=1`
Here, `|A| != 0`, so `A` is nonsingular matrix
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