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  • For the matrices A and B, verify that (AB)′ = B′A′, where (i)

Q5.    For the matrices A and B, verify that (AB)' = B'A', where

            (i)    A = \begin{bmatrix} 1\\-4 \\3 \end{bmatrix}, B = \begin{bmatrix} -1& 2 &1 \end{bmatrix}

Answers (1)

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  A = \begin{bmatrix} 1\\-4 \\3 \end{bmatrix},    B = \begin{bmatrix} -1& 2 &1 \end{bmatrix}

To prove : (AB)' = B'A'

L.H.S : (AB)'

AB = \begin{bmatrix} 1\\-4 \\3 \end{bmatrix}\begin{bmatrix} -1& 2 &1 \end{bmatrix}

AB = \begin{bmatrix} -1&2&1\\4&-8&-4 \\-3 &6&3\end{bmatrix}

(AB)' = \begin{bmatrix} -1&4&-3\\2&-8&6 \\1 &-4&3\end{bmatrix}

R.H.S : B'A'

B' = \begin{bmatrix} -1\\2 \\1 \end{bmatrix}

A' = \begin{bmatrix} 1& -4 &3 \end{bmatrix}

B'A' = \begin{bmatrix} -1\\2 \\1 \end{bmatrix}\begin{bmatrix} 1& -4 &3 \end{bmatrix}

B'A' = \begin{bmatrix} -1&4&-3\\2&-8&6 \\1&-4&3 \end{bmatrix}

Hence, L.H.S =R.H.S 

so it is verified that (AB)' = B'A'.

 

 

 

 

 

Posted by

seema garhwal

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