Let -1- vmatrix a1 -b1 -c1 11 a2 -b2 -c2 11a- 3 - b- 3 - c- 3vmatrix and Delta 2 - begin vmatrix lalpha2 -lend vmatrix - and -1-2 can be expressed as the sum of n determinants- then n -A- 3B- 27C- 2D- 9

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Byju's Answer

Standard XII

Mathematics

Evaluation of a Determinant

Let Δ1= vmatr...

Question

Let $Δ_{1}$ = $∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣$ and
$Δ_{2} = ∣ ∣ ∣ ∣ ∣ \begin{matrix} α_{1} & β_{1} & γ_{1} α_{2} & β_{2} & γ_{3} α_{3} & β_{3} & γ_{3} \end{matrix} ∣ ∣ ∣ ∣ ∣$ , and $Δ_{1} \times Δ_{2}$ can be expressed as the sum of $n$ determinants, then $n =$

$9$

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$3$

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$27$

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$2$

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Solution

The correct option is C
$27$

$Δ_{1} \times Δ_{2}$ is $3 \times 3$ determinant in which every element is sum of three terms.

$\Rightarrow$ It can be written as sum of
$3 \times 3 \times 3 = 27$ determinants

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Similar questions

If A1, B1, C1 … are the cofactors of the elements a1, b1, c1... of the matrix

$⎡ ⎢ ⎣ \begin{matrix} a 1 & b 1 & c 1 a 2 & b 2 & c 2 a 3 & b 3 & c 3 \end{matrix} ⎤ ⎥ ⎦$ then $∣ ∣ ∣ \begin{matrix} B 2 & C 2 B 3 & C 3 \end{matrix} ∣ ∣ ∣ =$

Q. Let

Δ_{1} = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣

and

Δ_{2} = ∣ ∣ ∣ ∣ ∣ \begin{matrix} α_{1} & β_{1} & γ_{1} α_{2} & β_{2} & γ_{2} α_{3} & β_{3} & γ_{3} \end{matrix} ∣ ∣ ∣ ∣ ∣

, then

Δ_{1} \times Δ_{2}

can be expressed as the sum of how many determinants?

Q. If

Δ_{1} = ∣ ∣ ∣ ∣ \begin{matrix} x & sin θ & cos θ - sin θ & - x & 1 cos θ & 1 & x \end{matrix} ∣ ∣ ∣ ∣

and

Δ_{2} = ∣ ∣ ∣ ∣ \begin{matrix} x & sin 2 θ & cos 2 θ - sin 2 θ & - x & 1 cos 2 θ & 1 & x \end{matrix} ∣ ∣ ∣ ∣

x \neq 0

; then for all

θ \in (0, \frac{π}{2})

I f x^{a} y^{b} = e^{m}, x^{c} y^{d} = e^{n}, Δ_{1} = ∣ ∣ ∣ \begin{matrix} m & b n & d \end{matrix} ∣ ∣ ∣ Δ_{2} = ∣ ∣ ∣ \begin{matrix} a & m c & n \end{matrix} ∣ ∣ ∣

and

Δ_{3} = ∣ ∣ ∣ \begin{matrix} a & b c & d \end{matrix} ∣ ∣ ∣,

then the values of x and y are respectively

Q. Let

Δ_{1} = ∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} + c^{2} & a b & a c a b & c^{2} + a^{2} & b c a c & b c & a^{2} + b^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

and

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

then

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Let Δ1=∣∣ ∣∣a1b1c1a2b2c2a3b3c3∣∣ ∣∣ and Δ2 =∣∣ ∣ ∣∣α1β1γ1α2β2γ3α3β3γ3∣∣ ∣ ∣∣, and Δ1×Δ2 can be expressed as the sum of n determinants, then n=

The correct option is C 27 Δ1×Δ2 is 3×3 determinant in which every element is sum of three terms. ⇒ It can be written as sum of 3×3×3=27 determinants

The correct option is C
$27$

$Δ_{1} \times Δ_{2}$ is $3 \times 3$ determinant in which every element is sum of three terms.

$\Rightarrow$ It can be written as sum of
$3 \times 3 \times 3 = 27$ determinants