Jitender Gupta and Divya Malik Solutions for Exercise 3: CHAPTER EXERCISE

If the matrix $A=\left[\begin{array}{ccc}a& 1& x\\ 2& \sqrt{3}& x^2-y\\ 0& 5& 2/5\end{array}\right]$' then write the number of elements.

If the matrix $P=\left[\begin{array}{ccc}1& 3& 4\\ \sqrt{5}& x& 0\\ y& 3/5& -3\end{array}\right]$' then write the number of elements.

If $\left[\begin{array}{cc}39& 5x+7y\\ 2x-5y& 41\end{array}\right]=\left[\begin{array}{cc}7u+9v& 1\\ 16& 9u+7\end{array}\right]$, then find the value of $x+y+u+v$.

If $\mathrm{A}=\left[\begin{array}{cc}\cot 45°& 0\\ -1& 1\end{array}\right] \& \mathrm{B}=\left[\begin{array}{cc}1& \cos 0°\\ 4& 5\end{array}\right]$, then find the value of the following: ${\mathrm{B}}^2-{\mathrm{A}}^2$.

If $\mathrm{A}=\left[\begin{array}{cc}\mathrm{p}& 0\\ 0& 2\end{array}\right], \mathrm{B}=\left[\begin{array}{cc}0& -\mathrm{q}\\ 1& 0\end{array}\right] \mathrm{and} \mathrm{C}=\left[\begin{array}{cc}2& -2\\ 2& 2\end{array}\right]$ and $\mathrm{BA}={\mathrm{C}}^2$, then find the value of $\mathrm{p}$ and $\mathrm{q}$.

If $\mathrm{A}=\left[\begin{array}{cc}2& -3\\ \mathrm{p}& \mathrm{q}\end{array}\right]$, then find $\mathrm{p}$ and $\mathrm{q}$, so that ${\mathrm{A}}^2=\mathrm{I}$.

 If $A=\left[\begin{array}{cc}3& 2\\ -1& 1\end{array}\right] and B=\left[\begin{array}{cc}14& 3\\ 2& 4\end{array}\right]$, then find the matrix $C$, such that $AC=B$.

If $\text{A = }\left[\begin{array}{cc}0& 1\\ -1& 0\end{array}\right]$, then find the real value of $\text{x and y}$, such that ${\left(\mathrm{xI}+\mathrm{yA}\right)}^2=\mathrm{A}$.