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Using the property of determinants and w...

Using the property of determinants and without expanding, prove that:`|[2, 7, 65],[ 3 ,8 ,75 ],[4, 9,86]|=0`

Text Solution

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`L.H.S. = |[2,7,65],[3,8,75],[5,9,86]|`
Applying `C_3->C_3-C_1`
`= |[2,7,63],[3,8,72],[5,9,81]|`
`=9|[2,7,7],[3,8,8],[5,9,9]|`
Applying `C_3->C_3-C_2`
`=9|[2,7,0],[3,8,0],[5,9,0]|`
If in a determinant, all elements in a row or column are `0`, then value of that determinant is `0`.
Here `C_3` is `0`.
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