Transpose Conjugate

Q. 5^{2x+1}÷25=125

Q.

Given $2A^{\ast }+B^{\ast }=\left[\begin{array}{cc}-2i& -4i\\ -6i& -8i\end{array}\right]$ and all the elements of B are 2. Then matrix A is given by. ($\ast$ represents transpose conjugate operator)

1. 

2. 

3. 

4. 

Q.

What is the transpose conjugate for the matrix. $\left[\begin{array}{cc}2+3i& -i\\ 5& 5-i\end{array}\right]$

1. 

2. 

3. 

4. 

Q. If A and B are symmetric matrices of same order and X= AB + BA and Y = AB – BA, then $(XY{)}^T$ is equal to

1. – YX
2. XY
3. YX
4. None of these

Q. $IfA=\left[\begin{array}{cc}cos\theta & sin\theta \\ sin\theta & -cos\theta \end{array}\right],B=\left[\begin{array}{cc}1& 0\\ -1& 1\end{array}\right],C=AB{A}^T,then{A}^T{C}^{n}Aequalsto\left(nϵZ^{+}\right)$

1. $\left[\begin{array}{cc}1& -n\\ 0& 1\end{array}\right]$
2. $\left[\begin{array}{cc}0& 1\\ 1& -n\end{array}\right]$
3. $\left[\begin{array}{cc}1& 0\\ -n& 1\end{array}\right]$
4. $\left[\begin{array}{cc}-n& 1\\ 1& 0\end{array}\right]$

Q.

If A and B are 2 matrices given by general elements $a_{ij}$ and $b_{ij}$ respectively. And $b_{ij}$ = Im($a_{ij}$). Then which the following are correct if A* + B = 0. ( Im(x) means Imaginary part of the number x)

1. A is a symmetric matrix

2. A is a non symmetric matrix

3. Sum of real parts of elements of A is zero

4. Sum of imaginary parts of elements of A is zero

Q. If A and B are symmetric matrices of same order and X= AB + BA and Y = AB – BA, then $(XY{)}^T$ is equal to

1. XY
2. YX
3. – YX
4. None of these

Q. if a^{1/a}=b^{1/b}=c^{1/c} and a^{bc}+b^{ac}+c^{ab}=729 , then find the value of b^{1/b