Using the property of determinants and without expanding- prove that- b-c q-r y-z- c-a r-p z-x- a-b p-q x-y -2- a p x- b q y- c r z -

Applying R2 → R2 − R3, we have: Applying R1 ↔R3 and R2 ↔R3, we have: Applying R1 → R1 − R3, we have: Applying R1 ↔R2 and R2 ↔R3, we have: From (1), (2), a ...

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Standard XII

Mathematics

Properties of Determinants

Using the pro...

Question

Using the property of determinants and without expanding, prove that:

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Solution

Applying R₂ → R₂ − R₃, we have:

Applying R₁ ↔R₃ and R₂ ↔R₃, we have:

Applying R₁→ R₁ − R₃, we have:

Applying R₁ ↔R₂ and R₂ ↔R₃, we have:

From (1), (2), and (3), we have:

Hence, the given result is proved.

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Using the property of determinants and without expanding, prove that:

Applying R2 → R2 − R3, we have: Applying R1 ↔R3 and R2 ↔R3, we have: Applying R1 → R1 − R3, we have: Applying R1 ↔R2 and R2 ↔R3, we have: From (1), (2), and (3), we have: Hence, the given result is proved.

Applying R₂ → R₂ − R₃, we have:

Applying R₁ ↔R₃ and R₂ ↔R₃, we have:

Applying R₁→ R₁ − R₃, we have:

Applying R₁ ↔R₂ and R₂ ↔R₃, we have:

From (1), (2), and (3), we have:

Hence, the given result is proved.