CBSE Class 12 Math 2018 Solved Paper

Question : 13 of 29

Marks: +1, -0

Using properties of determinants, prove that

|\table 1,1,1+3x;1+3y,1,1;1,1+3z,1|

= 9 (3xyz + xy + yz + zx)

Solution:

Let Δ =

|\table 1,1,1+3x;1+3y,1,1;1,1+3z,1|

Apply

R_2

→

R_2 - R_1

R_3

→

R_3 - R_1

Δ =

|\table 1,1,1+3x;3y,0,-3x;0,3z,-3x|

Expanding along

R_1

, we get
Δ = 9xz + 9xy + 9yz + 27xyz
= 9 (xz + xy + yz + 3xyz)

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