Q2 of 256 Page 7

Without expanding, show that the value of each of the following determinants is zero:



Applying R2→R2 – R1 and R3 → R3 – R1, we get,



Taking (b – a) and (c – a) common from R2 and R3 respectively,



= [(b – a)(c – a)][(c + a) – (b + a) – ( – b + c)]


= [(b – a)(c – a)][c + a + b – a – b – c]


= [(b – a)(c – a)][0] = 0


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