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Question

By using properties of determinants, show that:

(i)

(ii)

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Solution

(i)

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

Applying R1 → R1 + R2, we have:

Expanding along C1, we have:

Hence, the given result is proved.

(ii) Let.

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

Applying C1 → C1 + C2, we have:

Expanding along C1, we have:

Hence, the given result is proved.


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