Practice set first

1 ).  Make a matrix \(A=[a_{ij}]\) of order \( 3\times 3\) whose elements are of form \(\displaystyle a_{ij}=\frac{|i-j|}{j}\) 


2).  What are possible orders of matrices with 24 elements.


3).  Given \(A = \left(\begin{array}{cc} 1 & -3 \\ 8 & 2 \\ \end{array}\right)\), \(B=\left(\begin{array}{cc} -1 & 3 \\2 & -9 \\\end{array}\right)\), Find \(-2A+B\)?


4).  Given that \(A = \left(\begin{array}{cc} 1 & 0 \\ 8 & 2 \\ \end{array}\right)\), find the value of \(A^2+2A-I\)


5).   Given that \(A = \left(\begin{array}{ccc} 1 & 2 & 3 \\ 2 & 3 & 1 \\ \end{array}\right)\) and \(B = \left(\begin{array}{ccc} 3 & -1 & 3 \\ -1 & 0& 2 \\ \end{array}\right)\) then find \(2 A-B\).


6). Find the value of \(x\) and \(y\) if 

\[2\left[\begin{array}{cc}x & 5 \\7 & y-3\end{array}\right]+\left[\begin{array}{cc}3 & -4 \\1 & 2\end{array}\right]=\left[\begin{array}{cc}7 & 6 \\15 & 14\end{array}\right]\]


7). Find the value of \(AB\) given that \[A=\left[\begin{array}{ll}6 & 9 \\2 & 3\end{array}\right] \;\text { and }\; B=\left[\begin{array}{ccc}2 & 6 & 0 \\7 & 9 & 8\end{array}\right]\]







Answer 

1). \(\left(\begin{array}{ccc} 0 &\frac{1}{2} &\frac{2}{3} \\ 1 & 0 & \frac{1}{3} \\ 2 & \frac{1}{2} & 0  \\\end{array}\right)\)


2).\(12 \times 2\),  \(2 \times 12\),  \(6 \times 4\),  \(4 \times 6\),  \(24 \times 1\),  \(1 \times 24\), \(8 \times 3\) , \(3 \times 8\).


3). \(\left(\begin{array}{cc}-3 & 9 \\-14 & -13 \\\end{array}\right)\)


4). \(\left(\begin{array}{cc} 2 & 0 \\ 40 & 7 \\ \end{array}\right)\)


5).  \(\left(\begin{array}{ccc} -1 & 5 & 3 \\ 5 & 6 & 0 \\ \end{array}\right)\)


6). \(x=2\) and \(y=9\)


7). \(\left[\begin{array}{ccc}75 & 117 & 72 \\25 &39 & 24\end{array}\right]\)


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