If a1-a2-a3-a9 rae in H-P and a4-5-a5-5 then value of the determinant - -a1 a2 a3 a4 a5 a6 a6 a7 a8 equals

The correct option is D 0 =| a _ 1 amp; a _ 2 amp; a _ 3 a _ 4 amp; a _ 5 amp; a _ 6 a _ 7 amp; a _ 8 amp; a _ 9 ...

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Byju's Answer

Standard XII

Mathematics

Scalar Matrix

If a1,a2,a3...

Question

If $a_{1}, a_{2}, a_{3} . . . . a_{9}$ rae in H.P and $a_{4} = 5, a_{5} = 5$ then value of the determinant
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} a_{4} & a_{5} & a_{6} a_{6} & a_{7} & a_{8} \end{matrix} ∣ ∣ ∣ ∣$ equals

0

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2.5

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\frac{3}{20}

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\frac{7}{20}

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Solution

The correct option is D $0$
$△ = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} a_{4} & a_{5} & a_{6} a_{7} & a_{8} & a_{9} \end{matrix} ∣ ∣ ∣ ∣$
$a_{4} = 5; a_{5} = 5$
$a_{1,} a_{2}, a_{3}, a_{4}, a_{5}, . . ., a_{9}$ are in H.P
$∴ a_{1} = 5, a_{2} = 5, a_{3} = 5, a_{4} = 5, a_{5} = 5, a_{6} = 5, a_{7} = 5, a_{8} = 5, a_{9} = 5$
$△ = ∣ ∣ ∣ ∣ \begin{matrix} 5 & 5 & 5 5 & 5 & 5 5 & 5 & 5 \end{matrix} ∣ ∣ ∣ ∣ = 0$
$∵$ Any Two rows or columns of matrix are identical then its determinant = 0.

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Similar questions

Q. If

a_{1}, a_{2}, a_{3}, a_{4}, a_{5} > 0

then

\frac{a_{1}}{a_{2} + a_{3}} + \frac{a_{2}}{a_{3} + a_{4}} + \frac{a_{3}}{a_{4} + a_{5}} + \frac{a_{4}}{a_{5} + a_{1}} + \frac{a_{5}}{a_{1} + a_{2}} \geq \frac{5}{2}

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a_{1}, a_{2}, a_{3}, a_{4}, \dots

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a_{1} + a_{5} + a_{9} + . . . + a_{29} = 64

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