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Question -

By using properties ofdeterminants, show that:



Answer -


(i)   (ii) 


Solution

(i) 

Applying R1 → R1 − RandR2 → R2 − R3, we have:

Applying R1 → R1 + R2, we have:

Expanding along C1, we have:

Hence, the given resultis proved.


(ii) Let

Applying C1 → C1 − CandC2 → C2 − C3, we have:

Expanding along C1, we have:

Hence, the given resultis proved.


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