By using properties of determinants- show that- 0 a -b- -a 0 -c- b c 0 -0

We have, Here, the two rows R1 and R3 are identical. ∴Δ = 0. ...

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By using prop...

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By using properties of determinants, show that:

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∣ ∣ ∣ ∣ \begin{matrix} 0 & a & - b - a & 0 & - c b & c & 0 \end{matrix} ∣ ∣ ∣ ∣ = 0

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

∣ ∣ ∣ ∣ \begin{matrix} a - b - c & 2 a & 2 a 2 b & b - c - a & 2 b 2 c & 2 c & c - a - b \end{matrix} ∣ ∣ ∣ ∣ = {(a + b + c)}^{3}

a + b + c \neq 0

∣ ∣ ∣ ∣ \begin{matrix} a & b & c b & c & a c & a & b \end{matrix} ∣ ∣ ∣ ∣ = 0

a = b = c

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