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Question

Given 2A+B=[2i4i6i8i] and all the elements of B are 2. Then matrix A is given by. ( represents transpose conjugate operator)


A

[i2i3i4i]

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B

[1+i1+2i1+3i1+4i]

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C

[2+2i2+4i2+6i2+8i]

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D

[i13i12i14i1]

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Solution

The correct option is B

[1+i1+2i1+3i1+4i]


Given that 2A+B=[2i4i6i8i] and B=[2222]

Then 2A+2[1111]=[2i4i6i8i]

( SInce elements of B are all same and is equal to a real number B=B )

A=[2i12i13i14i1]A=(A)=[i13i12i14i1]

(This is a property. If conjugate transpose is done twice on a matrix you will get the original matrix)

Hence the option (b)


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