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

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

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

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

Q.

If A = $\left[\begin{array}{cc}0& 2\\ 3& 5\end{array}\right]$, B = $\left[\begin{array}{ccc}3& 4& 5\\ 2& 3& 1\\ 1& 3& 7\end{array}\right]$ then A + B =

1. 

2. 

3. None

4. 

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 = -------

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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

Q.

Which is the following is true about addition of matrices.

1. Addition of matrices can be performed only on two matrices of the same orders.

2. Addition of matrices can be performed on two matrices which are not necessarily of same order.

3. The resultant matrix obtained after addition of two matrices is of the same order as the order of two original matrices.

4. None of these

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= -----

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

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. $\mathrm{Let}A+2B=\left(\begin{array}{ccc}1& 2& 0\\ 6& -3& 3\\ -5& 3& 1\end{array}\right]\mathrm{and}2A-B=\left(\begin{array}{ccc}2& -1& 5\\ 2& -1& 6\\ 0& 1& 2\end{array}\right],\mathrm{then}\mathrm{find}\mathrm{tr}\left(A\right)-\mathrm{tr}\left(B\right).$

1. 3
2. -1
3. -3
4. 2

Q. $\left(\begin{array}{cc}2& 5\\ g& j\end{array}\right]+\left(\begin{array}{ccc}5& h& m\\ 4& 5& 6\end{array}\right]=$

1. Addition impossible
2. $\left(\begin{array}{cc}7& 5+h\\ 4+g& 5+j\end{array}\right]$
3. $\left(\begin{array}{ccc}7& 5+h& m\\ 4+g& 5+j& 6\end{array}\right]$