Embibe Experts Solutions for Chapter: Matrices, Exercise 1: Meghalaya Board-2018

Find the matrix $X$ such that$2A - B + X = 0$, where

$A =$$\left[\begin{array}{cc}3& 1\\ 0& 2\end{array}\right]$ and $B =\left[\begin{array}{cc}-2& 1\\ 0& 3\end{array}\right]$

If $A=\left[\begin{array}{cc}1& 3\\ -2& 5\end{array}\right]$ and $B=\left[\begin{array}{cc}-2& 5\\ 3& 4\end{array}\right]$, then find $A-4B$.

Express the matrix $A=\left[\begin{array}{cc}2& 3\\ -1& 4\end{array}\right]$ as a sum of a symmetric and a skew-symmetric matrix.
 

Construct a $2\times 2$ matrix $A=\left[a_{ij}\right]$, whose elements are given by $a_{ij}=\frac{(i+j{)}^2}{2}$;

If $A=\left[\begin{array}{lll}1& 2& 3\\ 2& 3& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}3& -1& 3\\ -1& 0& 2\end{array}\right]$ then find $2A-B.$

Which of the given values of $x$ and $y$ make the following pair of matrices equal?

$\left[\begin{array}{cc}3x+7& 5\\ y+1& 2-3x\end{array}\right]$ and $\left[\begin{array}{cc}0& y-2\\ 8& 4\end{array}\right]$

Obtain the inverse of the following matrix using elementary operations : $A=\left[\begin{array}{lll}0& 1& 2\\ 1& 2& 3\\ 3& 1& 1\end{array}\right]$

Find the values of $x,y,z$ if $\left[\begin{array}{c}x+y+z\\ x+z\\ y+z\end{array}\right]=\left[\begin{array}{c}9\\ 5\\ 7\end{array}\right]$.