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Evaluate: \(\begin{vmatrix} a + x & y & z \\[0.3em] x&a + y & z \\[0.3em] x & y&a + z \end{vmatrix}\)

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Evaluate: \(\begin{vmatrix} a + x & y & z \\[0.3em] x&a + y & z \\[0.3em] x & y&a + z \end{vmatrix}\)

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1 Answer

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Best answer

Suppose

On applying row operation R1 → R1 - R2, and R3 → R3 - R2

On applying column operation C2 → C2 - C1

= a[a (a + x + y) + az] + 0 + 0

= a2(a + x + y + z)

Therefore, Δ = a2(a + x + y + z)

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