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  • How to solve this problem- - Matrices and Determinants - JEE Main-3

What is the transpose conjugate of  \begin{bmatrix} i+3 &i-3 \\0 & i+1 \end{bmatrix}?

  • Option 1)

    \begin{bmatrix} i+3 &i+3 \\0 & i+1 \end{bmatrix}

  • Option 2)

    \begin{bmatrix} i-3 &0 \\i+3 & i-1 \end{bmatrix}

  • Option 3)

    \begin{bmatrix} -i+3 &-i-3 \\0 & -i+1 \end{bmatrix}

  • Option 4)

    \begin{bmatrix} i+3 &-i-3 \\0 & -i+1 \end{bmatrix}

 

Answers (1)

best_answer

As we learnt

 

Transpose conjugate of a Matrix -

 

The transpose of the conjugate of a matrix

- wherein

It is denoted by   A^{\Theta } and  \left ( A{}' \right )= A^{\Theta } 

 

 

 

A=\begin{bmatrix} i+3 &i-3 \\0 & i+1 \end{bmatrix}

\overline{A}=\begin{bmatrix} -i+3 &-i-3 \\0 & -i+1 \end{bmatrix}

\left ( \overline{A} \right ){}'=\begin{bmatrix} -i+3 &-i-3 \\0 & -i+1 \end{bmatrix}

 


Option 1)

\begin{bmatrix} i+3 &i+3 \\0 & i+1 \end{bmatrix}

Option 2)

\begin{bmatrix} i-3 &0 \\i+3 & i-1 \end{bmatrix}

Option 3)

\begin{bmatrix} -i+3 &-i-3 \\0 & -i+1 \end{bmatrix}

Option 4)

\begin{bmatrix} i+3 &-i-3 \\0 & -i+1 \end{bmatrix}

Posted by

Himanshu

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