R D Sharma Solutions for Chapter: Algebra of Matrices, Exercise 1: EXERCISE

If$A=\left[a_{ij}\right]=\left[\begin{array}{rrr}2& 3& -5\\ 1& 4& 9\\ 0& 7& -2\end{array}\right]$and $B=\left[b_{ij}\right]=\left[\begin{array}{rr}2& -1\\ -3& 4\\ 1& 2\end{array}\right]$ then find $a_{22}+b_{21}$

If$A=\left[a_{ij}\right]=\left[\begin{array}{rrr}2& 3& -5\\ 1& 4& 9\\ 0& 7& -2\end{array}\right]$and $B=\left[b_{ij}\right]=\left[\begin{array}{rr}2& -1\\ -3& 4\\ 1& 2\end{array}\right]$
then find $a_{11}{b}_{11}+a_{22}{b}_{22}$

Construct a $3\times 4$ matrix $A=\left[a_{ij}\right]$ whose elements $a_{ij}$ are given by:

$a_{ij}=2i$

Find $x, y, a$ and $b$ if $\left[\begin{array}{ccc}2x-3y& a-b& 3\\ 1& x+4y& 3a+4b\end{array}\right]=\left[\begin{array}{rrr}1& -2& 3\\ 1& 6& 29\end{array}\right]$

The sales figure of two car dealers during January $2013$ showed that dealer $A$ sold $5$ deluxe, $3$ premium and $4$ standard cars, while dealer$B$ sold $7$ deluxe, $2$ premium and $3$ standard cars. Total sales over the $2$ month period of January-February revealed that dealer $A$ sold $8$ deluxe $7$ premium and $6$ standard cars. In the same $2$ month period, dealer $B$ sold $10$ deluxe, $5$ premium and $7$ standard cars. Write $2\times 3$ matrices summarizing sales data for January and $2$-month period for each dealer.

For what values of $x$ and $y$ are the following matrices equal?

$A=\left[\begin{array}{cc}2x+1& 2y\\ 0& y^2-5y\end{array}\right], B=\left[\begin{array}{cc}x+3& y^2+2\\ 0& -6\end{array}\right]$

Find the values of  $x$   and   $y$  if $\left[\begin{array}{cc}x+10& y^2+2y\\ 0& -4\end{array}\right]=\left[\begin{array}{cc}3x+4& 3\\ 0& y^2-5y\end{array}\right]$

For what values of  $a$ and $b$ if $A=B$, where $A=\left[\begin{array}{cc}a+4& 3b\\ 8& -6\end{array}\right],B=\left[\begin{array}{cc}2a+2& b^2+2\\ 8& b^2-10\end{array}\right]$