By using properties of determinants- show that- -a2 a b a c- b a -b2 b c- c a c b -c2 -4 a2 b2 c2

Applying R2 → R2 + R1 and R3 → R3 + R1, we have: ...

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Evaluation of a Determinant

By using prop...

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By using properties of determinants, show that:

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∣ ∣ ∣ ∣ ∣ \begin{matrix} - a^{2} & a b & a c a b & - b^{2} & b_{C} a c & b_{C} & - c^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ ∣ \begin{matrix} {- a}^{2} & a b & a c b a & {- b}^{2} & b c c a & c b & {- c}^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = {4 a}^{2} b^{2} c^{2}

∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} & b c & a c + c^{2} a^{2} + a b & b^{2} & a c a b & b^{2} + b c & c^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = 4 a^{2} b^{2} c^{2}

By using properties of determinants, show that:

∣ ∣ ∣ ∣ \begin{matrix} a & b - c & c + b a + c & b & c - a a - b & b + a & c \end{matrix} ∣ ∣ ∣ ∣ = (a + b + c) (a^{2} + b^{2} + c^{2})

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