Q. 11 A4.6( 39 Votes )

# By using properties of determinants, show that:

C1 C1 + C2 + C3 (i.e. replace 1st column by addition of 1st, 2nd and 3rd column)

Taking 2(x + y + z) outside the determinant from 1st column

R2 R2 - R1 (i.e. replace 2nd row by subtraction of 2nd and 1st row)

R3 R3 - R1 (i.e. replace 3rd row by subtraction of 3rd and 1st row)

Expanding the determinant along 1st column

LHS = 2(x + y + z)3 = RHS

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