Q15 of 29 Page 1

Using properties of determinants, prove:


LHS


Let R1→ R1 + R2 + R3



Taking (5x + 4) as a common factor,



Applying C1→ C1 – C2 and C2→ C2 – C3



Taking (x – 4) as a common factor from C2,



Expanding along R1, we get,


LHS = (5x + 4) (x – 4) [1(x + 4) – 2x(1)]


= (5x + 4) (x – 4) (4 – x)


= (5x + 4) (4 – x)2


= RHS


So, LHS = RHS


Hence, proved.


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