Question

Without expanding at any stage, find the value of:

`|(a,b,c),(a+2x,b+2y,c+2z),(x,y,z)|`

Answer 1

`|(a,b,c),(a+2x,b+2y,c+2z),(x,y,z)|`

`R_1"/"R_1 + R_3, R_2"/"R_2-R_3`

`= |(a+x, b+y,c+z),(a+x,b+y,c+z),(x,y,z)| = 0`    (∵ R₁ =   R₂)