The matrices P=[u1v1w1u2v2w2u3v3w3];Q=19[22113−5m−815] are such that PQ=I ,an identity matrix. solving the equation [u1v1w1u2v2w2u3v3w3][xyz]=[115] ,the value of y comes out to be −3 .then the value of m is equal to

PQ=I⇒P−1=Q now the system in matrix notation is PX=B⇒X=P-1B∴[xyz]=19[22113−5m−815][115]∴y=19(13−5+5m)⇒-27=8+5m∴m=−7

The matrices P=[u1v1w1u2v2w2u3v3w3];Q=19[22113−5m−815] are such that PQ=I ,an identity matrix. solving the equation [u1v1w1u2v2w2u3v3w3][xyz]=[115] ,the value of y comes out to be −3 .then the value of m is equal to

PQ=I⇒P−1=Q now the system in matrix notation is PX=B⇒X=P-1B∴[xyz]=19[22113−5m−815][115]∴y=19(13−5+5m)⇒-27=8+5m∴m=−7

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The matrices $P = [\begin{matrix} u_{1} & v_{1} & w_{1} \\ u_{2} & v_{2} & w_{2} \\ u_{3} & v_{3} & w_{3} \end{matrix}]; Q = \frac{1}{9} [\begin{matrix} 2 & 2 & 1 \\ 13 & - 5 & m \\ - 8 & 1 & 5 \end{matrix}]$ are such that $P Q = I$ ,an identity matrix. solving the equation $[\begin{matrix} u_{1} & v_{1} & w_{1} \\ u_{2} & v_{2} & w_{2} \\ u_{3} & v_{3} & w_{3} \end{matrix}] [\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} 1 \\ 1 \\ 5 \end{matrix}]$ ,the value of y comes out to be $- 3$ .then the value of m is equal to

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$- 27$

$- 7$

answer is D.

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$P Q = I \Rightarrow P^{- 1} = Q$

$n o w t h e s y s t e m i n m a t r i x n o t a t i o n i s P X = B$ $\Rightarrow X = P^{- 1} B$

$∴ [\begin{matrix} x \\ y \\ z \end{matrix}] = \frac{1}{9} [\begin{matrix} 2 & 2 & 1 \\ 13 & - 5 & m \\ - 8 & 1 & 5 \end{matrix}] [\begin{matrix} 1 \\ 1 \\ 5 \end{matrix}]$

$∴ y = \frac{1}{9} (13 - 5 + 5 m)$

$\Rightarrow - 27 = 8 + 5 m$

$∴ m = - 7$

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The matrices P=[u1v1w1u2v2w2u3v3w3];Q=19[22113−5m−815] are such that PQ=I ,an identity matrix. solving the equation [u1v1w1u2v2w2u3v3w3][xyz]=[115] ,the value of y comes out to be −3 .then the value of m is equal to

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