If A= \begin{bmatrix} 1 &2 \\ 3& -5 \end{bmatrix} ,If\, \, B= \begin{bmatrix} 1 &0 \\ 0& 2\end{bmatrix}  and x  is a matrix such that A= bx then x  equals to

  • Option 1)

    \frac{1}{2} \begin{bmatrix} -2 &4 \\ 3& 5 \end{bmatrix}

  • Option 2)

    \frac{+1}{2}\begin{bmatrix} 2 &4 \\ 3& -5\end{bmatrix}

  • Option 3)

    \begin{bmatrix} 2 &4\\ 3& -5 \end{bmatrix}

  • Option 4)

    None of these

 

Answers (1)

As learnt in concept

Inverse of a matrix -

 A^{-1}=\frac{1}{\left | A \right |}\cdot adjA

-

 

 A=BX

B^{-1}A=B^{-1}BX

B^{-1}A=X

B= \begin{bmatrix} 1 &0 \\ 0& 2 \end{bmatrix}                 \left | B \right |=2

adj B= \begin{bmatrix} 2 &0 \\ 0& 1 \end{bmatrix}         B^{-1}= \frac{1}{2}\begin{bmatrix} 2 &0 \\ 0& 1 \end{bmatrix}

Thus\ X = B^{-1}A

 =\frac{1}{2}\begin{bmatrix} 2 &0 \\ 0& 1 \end{bmatrix}\begin{bmatrix} 1 &2 \\ 3& -5 \end{bmatrix}

= \frac{1}{2}\begin{bmatrix} 2& 4\\ 3& -5 \end{bmatrix}

 


Option 1)

\frac{1}{2} \begin{bmatrix} -2 &4 \\ 3& 5 \end{bmatrix}

Incorrect option

Option 2)

\frac{+1}{2}\begin{bmatrix} 2 &4 \\ 3& -5\end{bmatrix}

Correct option

Option 3)

\begin{bmatrix} 2 &4\\ 3& -5 \end{bmatrix}

Incorrect option

Option 4)

None of these

Incorrect option

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