If - -b2-ab b-c bc-ac ab-a2 a-b b2-ab bc-ac c-a ab-a2 then - equals

The correct option is D 0 Δ = b^ 2 ab amp; b c amp; bc ac ab a^ 2 amp; a b amp; b^ 2 ab bc ac amp; c a amp; ab a^ 2 = ...

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Byju's Answer

Standard XII

Mathematics

Evaluation of a Determinant

If Δ =b2-ab...

Question

If $Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} - a b & b - c & b c - a c a b - a^{2} & a - b & b^{2} - a b b c - a c & c - a & a b - a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣$ then $Δ$ equals

(b - c) (c - a) (a - b)

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a b c (b - c) (c - a) (a - b)

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(a + b + c) (b - c) (c - a) (a - b)

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0

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Solution

The correct option is D $0$
$Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} - a b & b - c & b c - a c a b - a^{2} & a - b & b^{2} - a b b c - a c & c - a & a b - a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} & b & b c a b & a & b^{2} b c & c & a b \end{matrix} ∣ ∣ ∣ ∣ ∣ - ∣ ∣ ∣ ∣ ∣ \begin{matrix} a b & c & a c a^{2} & b & a b a c & a & a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = b^{2} ∣ ∣ ∣ ∣ \begin{matrix} b & b & c a & a & b c & c & a \end{matrix} ∣ ∣ ∣ ∣ - a^{2} ∣ ∣ ∣ ∣ \begin{matrix} b & c & c a & b & b c & a & a \end{matrix} ∣ ∣ ∣ ∣ = 0 - 0 = 0$

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Similar questions

The determinant
$∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} - a b & b - c & b c - a c a b - a^{2} & a - b & b^{2} - a b b c - a c & c - a & a b - a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣$ equals to:

(a) abc(b-c)(c-a)(a-b)
(b) (b-c)(c-a)(a-b)
(c) (a+b+c)(b-c)(c-a)(a-b)
(d) None of these

$a^{2} + b c + a b + a c = ? (a) (a + b) (a + c) (b) (a + b) (b + c) (c) (b + c) (c + a) (d) a (a + b + c)$

Q. Tick (✓) the correct answer:
a² + bc + ab + ac = ?
(a) (a + b)(a + c)
(b) (a + b)(b + c)
(c) (b + c)(c + a)
(d) a(a + b + c)

Q. If

a, b, c

and

A, B, C \in R - (0}

such that

a A + b B + c C + \sqrt{(a^{2} + b^{2} + c^{2}) (A^{2} + B^{2} + C^{2})} = 0

, then value of

\frac{a B}{b A} + \frac{b C}{c B} + \frac{c A}{a C}

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

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If Δ=∣∣ ∣ ∣∣b2−abb−cbc−acab−a2a−bb2−abbc−acc−aab−a2∣∣ ∣ ∣∣ then Δ equals

If $Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} - a b & b - c & b c - a c a b - a^{2} & a - b & b^{2} - a b b c - a c & c - a & a b - a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣$ then $Δ$ equals