If Nbeginbmatrix 18211384lendbmatrix Albegin bmatrix -385 12 -4lend bmatrix - begin bmatrix 18-5 118-27end bmatrix - then the matrix A is equal toA- -dfrac14beginbmatrix -4 - 11118 - 4lendbmatrix -183 182lendbmatrix -4 - 11 12 - 1 e n d b m a t r i x -183 12 - 1lendbmatrix

The correct option is D [ 1 amp;3; 2 amp;1 ]Let B=[ 1 amp;2; 3 amp;4 ],C=[ 3 amp;5; 2 amp; 4 ] and D=[ 1 amp; 5; 11 amp ...

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Byju's Answer

Standard XII

Mathematics

Transpose of a Matrix

If Nbeginbmat...

Question

If $[\begin{matrix} 1 & 2 3 & 4 \end{matrix}] A [\begin{matrix} - 3 & 5 2 & - 4 \end{matrix}] = [\begin{matrix} 1 & - 5 11 & - 27 \end{matrix}]$ , then the matrix $A$ is equal to

\frac{1}{4} [\begin{matrix} - 4 & 11 8 & 4 \end{matrix}]

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[\begin{matrix} - 1 & 3 1 & 2 \end{matrix}]

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\frac{1}{4} [\begin{matrix} - 4 & 11 12 & 1 \end{matrix}]

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[\begin{matrix} - 1 & 3 2 & 1 \end{matrix}]

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Solution

The correct option is D $[\begin{matrix} - 1 & 3 2 & 1 \end{matrix}]$
$Let B = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}], C = [\begin{matrix} - 3 & 5 2 & - 4 \end{matrix}] and D = [\begin{matrix} 1 & - 5 11 & - 27 \end{matrix}]$

$B A C = D \Rightarrow A C = B^{- 1} D$
$A = B^{- 1} D C^{- 1}$
$B^{- 1} = - \frac{1}{2} [\begin{matrix} 4 & - 2 - 3 & 1 \end{matrix}], C^{- 1} = - \frac{1}{2} [\begin{matrix} 4 & 5 2 & 3 \end{matrix}]$
$A = \frac{1}{4} [\begin{matrix} 4 & - 2 - 3 & 1 \end{matrix}] [\begin{matrix} 1 & - 5 11 & - 27 \end{matrix}] [\begin{matrix} 4 & 5 2 & 3 \end{matrix}]$
$= \frac{1}{4} [\begin{matrix} - 18 & 34 8 & - 12 \end{matrix}] [\begin{matrix} 4 & 5 2 & 3 \end{matrix}]$
$= \frac{1}{4} [\begin{matrix} - 4 & 12 8 & 4 \end{matrix}] = [\begin{matrix} - 1 & 3 2 & 1 \end{matrix}]$

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If [1234]A[−352−4]=[1−511−27], then the matrix A is equal to

The correct option is D [−1321]Let B=[1234],C=[−352−4]and D=[1−511−27] BAC=D⇒AC=B−1D A=B−1DC−1 B−1=−12[4−2−31],C−1=−12[4523] A=14[4−2−31][1−511−27][4523] =14[−18348−12][4523] =14[−41284]=[−1321]

If $[\begin{matrix} 1 & 2 3 & 4 \end{matrix}] A [\begin{matrix} - 3 & 5 2 & - 4 \end{matrix}] = [\begin{matrix} 1 & - 5 11 & - 27 \end{matrix}]$ , then the matrix $A$ is equal to