If p-q-r-0-a-b-c- then the value of the determinant beginvmatrixpa - qb - rcllqc - ra - pbilrb - pc - qa end vmatrix is

The correct option is D 0pq amp; qb amp; rc qc amp; ra amp; pb rb amp; pc amp; qa =pqr(a^3+b^3+c^3) abc(p^3+q^3+r^3)=pqr(3abc) abc(3pqr)= ...

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Byju's Answer

Standard XII

Mathematics

Inverse of a Matrix

If p+q+r=0=a+...

Question

If p + q + r = 0 = a + b + c, then the value of the determinant
$∣ ∣ ∣ ∣ \begin{matrix} p a & q b & r c q c & r a & p b r b & p c & q a \end{matrix} ∣ ∣ ∣ ∣$ is

pq + qb + rc

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none of these

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Solution

$∣ ∣ ∣ ∣ \begin{matrix} p q & q b & r c q c & r a & p b r b & p c & q a \end{matrix} ∣ ∣ ∣ ∣ = p q r (a^{3} + b^{3} + c^{3}) - a b c (p^{3} + q^{3} + r^{3}) = p q r (3 a b c) - a b c (3 p q r) = 0$

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Similar questions

Q. If

p + q + r = 0 = a + b + c,

then the value of the determinant

∣ ∣ ∣ ∣ \begin{matrix} p a & q b & r c q c & r a & p b r b & p c & q a \end{matrix} ∣ ∣ ∣ ∣

Q. If

p + q + r = 0 = a + b + c

, then the value of the determinant

∣ ∣ ∣ ∣ \begin{matrix} p a & q b & r c q c & r a & p b r b & p c & q a \end{matrix} ∣ ∣ ∣ ∣

If p + q + r = a + b + c = 0, then the determinant
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} p a & q b & r c q c & r a & p b r b & p c & q a \end{matrix} ∣ ∣ ∣ ∣$ equals

Q. If

p + q + r = a + b + c = 0

, then the determinant

∣ ∣ ∣ ∣ \begin{matrix} p a & q b & r c q c & r a & p b r b & p c & q a \end{matrix} ∣ ∣ ∣ ∣

equals.

If p + q + r = a + b + c = 0, then the determinant
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} p a & q b & r c q c & r a & p b r b & p c & q a \end{matrix} ∣ ∣ ∣ ∣$ equals

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If p + q + r = 0 = a + b + c, then the value of the determinant ∣∣ ∣∣paqbrcqcrapbrbpcqa∣∣ ∣∣ is

∣∣ ∣∣pqqbrcqcrapbrbpcqa∣∣ ∣∣=pqr(a3+b3+c3)−abc(p3+q3+r3)=pqr(3abc)−abc(3pqr)=0

If p + q + r = 0 = a + b + c, then the value of the determinant
$∣ ∣ ∣ ∣ \begin{matrix} p a & q b & r c q c & r a & p b r b & p c & q a \end{matrix} ∣ ∣ ∣ ∣$ is

$∣ ∣ ∣ ∣ \begin{matrix} p q & q b & r c q c & r a & p b r b & p c & q a \end{matrix} ∣ ∣ ∣ ∣ = p q r (a^{3} + b^{3} + c^{3}) - a b c (p^{3} + q^{3} + r^{3}) = p q r (3 a b c) - a b c (3 p q r) = 0$