If  then adj \left ( 3A^{2} +12A\right )  is equal to :

 

  • Option 1)

  • Option 2)

  • Option 3)

  • Option 4)

 

Answers (1)

As we leant in

Multiplication of matrices -

-

 

 

 

Adjoint of a square matrix -

Transpose of the matrix of co-factors of elements of A is called the adjoint of A

- wherein

 

 

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

\therefore A^2=\begin{bmatrix} 2 & -3\\ -4 & 1 \end{bmatrix} \begin{bmatrix} 2 & -3\\ -4 & 1 \end{bmatrix} = \begin{bmatrix} 16 & -9\\ -12 & 13 \end{bmatrix}

3 A^{2}+12 A=\begin{bmatrix} 48 & -27\\ -36 & 39 \end{bmatrix} + \begin{bmatrix} 24 & -36\\ -48 & 12 \end{bmatrix} \\ = \begin{bmatrix} 72 & -63\\ -84 & 51 \end{bmatrix}  

adj A= Transpose of cofactors

so that \begin{bmatrix} 51 & 63\\ 84 & 72 \end{bmatrix}


Option 1)

This option is correct.

Option 2)

This option is incorrect.

Option 3)

This option is incorrect.

Option 4)

This option is incorrect.

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