1 amp; a amp; b a amp; 1 amp; c b amp; c amp; 1 =1(1+c^2) a( a+bc)+b(ac+b) =1+a^2+b^2+c^2. ...

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Evaluation of a Determinant

1 a b-a ...

Question

$∣ ∣ ∣ ∣ \begin{matrix} 1 & a & b - a & 1 & c - b & - c & 1 \end{matrix} ∣ ∣ ∣ ∣ =$

1 + a^{2} + b^{2} + c^{2}

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1 - a^{2} + b^{2} + c^{2}

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1 + a^{2} + b^{2} - c^{2}

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1 + a^{2} - b^{2} + c^{2}

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Solution

The correct option is A $1 + a^{2} + b^{2} + c^{2}$
$∣ ∣ ∣ ∣ \begin{matrix} 1 & a & b - a & 1 & c - b & - c & 1 \end{matrix} ∣ ∣ ∣ ∣ = 1 (1 + c^{2}) - a (- a + b c) + b (a c + b) = 1 + a^{2} + b^{2} + c^{2}$ .

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Similar questions

∣ ∣ ∣ ∣ \begin{matrix} 1 & a & b - a & 1 & c - b & - c & 1 \end{matrix} ∣ ∣ ∣ ∣ =

⎛ ⎜ ⎝ \begin{matrix} 1 & a & b - a & 1 & c - b & - c & 1 \end{matrix} ⎞ ⎟ ⎠ = 1 + a^{2} + b^{2} + c^{2}

1 A B + C C A = 295

B

∣ ∣ ∣ ∣ \begin{matrix} 1 & a & b + c 1 & b & c + a 1 & c & a + b \end{matrix} ∣ ∣ ∣ ∣

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