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Find the conjugate of matrix \text{A}=\left[\begin{array}{ccc}{2 i} & {3+4 i} & {7} \\ {3+4 i} & {9} & {4+5 i} \\ {7} & {4+5 i} & {3+7 i}\end{array}\right]

Option: 1

\left[\begin{array}{ccc}{2 i} & {3i-4 } & {7i} \\ {3i-4 } & {9i} & {4i+5 } \\ {7i} & {4i-5 } & {3i-7 }\end{array}\right]


Option: 2

\left[\begin{array}{ccc}{-2 i} & {3-4 i} & {7} \\ {3-4 i} & {9} & {4+5 i} \\ {7} & {4-5 i} & {3-7 i}\end{array}\right]


Option: 3

\left[\begin{array}{ccc}{-2 i} & {3-4 i} & {7} \\ {3-4 i} & {9} & {4+5 i} \\ {7} & {4+5 i} & {3+7 i}\end{array}\right]


Option: 4

\left[\begin{array}{ccc}{-2 i} & {3+4 i} & {7} \\ {3+4 i} & {9} & {4+5 i} \\ {7} & {4-5 i} & {3-7 i}\end{array}\right]


Answers (1)

best_answer

 

 

Conjugate of a Matrix -

If a matrix A has a complex number as it’s elements, then the matrix obtained by replacing those complex number by its conjugate is called conjugate of the matrix A and it is denoted by \\\mathrm{\overline{A}}. (If the element of a matrix is a + ib, then it is replaced by a - ib .)
 

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\begin{array}{l}{ \mathrm{A}=\left[\begin{array}{ccc}{2 i} & {3+4 i} & {7} \\ {3+4 i} & {9} & {4+5 i} \\ {7} & {4+5 i} & {3+7 i}\end{array}\right] \text { then, }} \\\\ {\overline{\mathrm{A}}=\left[\begin{array}{ccc}{-2 i} & {3-4 i} & {7} \\ {3-4 i} & {9} & {4+5 i} \\ {7} & {4-5 i} & {3-7 i}\end{array}\right]}\end{array}

hence option (b) is correct

Posted by

manish painkra

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