Addition and Subtraction of a Matrix

Q.

If 3X + 2Y = I and 2X - Y = O, where I and O are unit and null matrices of order 3 respectively, then

1. $X=\left(\frac{1}{7}\right)I,Y=\left(\frac{2}{7}\right)$

2. $X=\left(\frac{2}{7}\right),Y=\left(\frac{1}{7}\right)I$

3. $X=\left(\frac{1}{7}\right)I,Y=\left(\frac{2}{7}\right)I$

4. $X=\left(\frac{2}{7}\right)I,Y=\left(\frac{1}{7}\right)I$

Q. Let A be a square matrix of order two such that $A-A{A}^T=I_2$. If trace $\left(A\right)\ne R$ and entries are complex numbers, number of such matrices possible are

Q.

If A = $\left[\begin{array}{ccc}2& 4& 8\\ 6& 9& 1\\ 8& 7& 5\end{array}\right]$ and B = $\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$ then the third element of the first row of A - B = -------

___

Q. If $A=\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& 2\\ 2& 2& 1\end{array}\right]$
and $|(A^2-pA-qI)|=0$, then $p+q=$

1. $9$
2. $8$
3. $7$
4. $10$

Q.

If A = $\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$ and B = $\left[\begin{array}{ccc}4& 5& 6\\ 7& 8& 9\\ 1& 2& 3\end{array}\right]$ then the order of A+B will be nxn where n= -----

___

Q. $\left(\begin{array}{cc}1& 2+3i\\ 2-3i& 5\end{array}\right]+\left(\begin{array}{cc}2i& 0\\ 5& 2\end{array}\right]=$

1. $\left(\begin{array}{cc}1+2i& 2+3i\\ 7-3i& 7\end{array}\right]$
2. $Additionisnotpossible$
3. $\left(\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$
4. $\left(\begin{array}{cc}9i& 9i\\ i& 0\end{array}\right]$

Q.

Find X if $2X+3Y=\left[\begin{array}{cc}2& 3\\ 4& 0\end{array}\right]and3X+2Y=\left[\begin{array}{cc}7& -2\\ -1& 5\end{array}\right]$

1. $\left[\begin{array}{cc}\frac{-2}{5}& \frac{12}{5}\\ \frac{11}{5}& -3\end{array}\right]$

2. $\left[\begin{array}{cc}\frac{2}{5}& \frac{-12}{5}\\ \frac{-11}{5}& 3\end{array}\right]$

3. $\left[\begin{array}{cc}\frac{2}{5}& \frac{13}{5}\\ \frac{14}{5}& -2\end{array}\right]$

4. $\left[\begin{array}{cc}\frac{-2}{5}& \frac{-13}{5}\\ \frac{-14}{5}& 2\end{array}\right]$

Q. Let A be a square matrix of order two such that $A-A{A}^T=I_2$. If trace $\left(A\right)\ne R$ and entries are complex numbers, number of such matrices possible are

Q. If $A^2=3A-2I$ and $A^8=aA+bI$, then $a+b$ is

1. 7
2. -1
3. 1
4. \N

Q.

If A = $\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$ and B = $\left[\begin{array}{ccc}4& 5& 6\\ 7& 8& 9\\ 1& 2& 3\end{array}\right]$ then the order of A+B will be nxn where n= -----

___

Q.

If A = $\left[\begin{array}{ccc}2& 4& 8\\ 6& 9& 1\\ 8& 7& 5\end{array}\right]$ and B = $\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$ then the third element of the first row of A - B = -------

___

Q.

Let A = $\left[\begin{array}{cc}1& 6\\ 2& 5\end{array}\right]$, B = $\left[\begin{array}{cc}3& 4\\ 4& 9\end{array}\right]$ then A + B =$$\left[\begin{array}{cc}4& 6\\ 10& 14\end{array}\right]$$

1. True

2. False