The value of determinant -a b ca-2x b-2y c-2zx y z is

The given determinant can be written as, Δ= a amp;b amp;c a amp;b amp;c x amp;y amp;z +2 a amp;b amp;c x amp;y amp;z x amp;y amp; ...

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Byju's Answer

Standard XII

Mathematics

Properties of Composite Function

The value of ...

Question

The value of determinant $Δ = ∣ ∣ ∣ ∣ \begin{matrix} a & b & c a + 2 x & b + 2 y & c + 2 z x & y & z \end{matrix} ∣ ∣ ∣ ∣$ is

x y z

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a b c

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2 x y z + a b c

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0

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Solution

The correct option is D $0$
The given determinant can be written as,
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} a & b & c a & b & c x & y & z \end{matrix} ∣ ∣ ∣ ∣ + 2 ∣ ∣ ∣ ∣ \begin{matrix} a & b & c x & y & z x & y & z \end{matrix} ∣ ∣ ∣ ∣ = 0 + 2 \cdot 0 = 0$
$∵ R_{1}$ and $R_{2}$ are identical in first determinant.
Similarly, $R_{2}$ and $R_{3}$ are identical in second determinant.

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The value of determinant Δ=∣∣ ∣∣abca+2xb+2yc+2zxyz∣∣ ∣∣ is

The correct option is D 0The given determinant can be written as, Δ=∣∣ ∣∣abcabcxyz∣∣ ∣∣+2∣∣ ∣∣abcxyzxyz∣∣ ∣∣ =0+2⋅0=0 ∵R1 and R2 are identical in first determinant. Similarly, R2 and R3 are identical in second determinant.

The value of determinant $Δ = ∣ ∣ ∣ ∣ \begin{matrix} a & b & c a + 2 x & b + 2 y & c + 2 z x & y & z \end{matrix} ∣ ∣ ∣ ∣$ is