Exercise

$A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$. Verify closure property of matrix multiplication with scalar $-2$.

Find a matrix $A$ such that $2A-3B+5C=0$, where $B=\left[\begin{array}{rrr}-2& 2& 0\\ 3& 1& 4\end{array}\right]$ and $C=\left[\begin{array}{rrr}2& 0& -2\\ 7& 1& 6\end{array}\right]$

Find main diagonal elements and determinant of $\left[\begin{array}{ll}3& 5\\ 4& 6\end{array}\right]$.

Find main diagonal elements and determinant of $\left[\begin{array}{ll}3& 2\\ 2& 6\end{array}\right]$.

What is a scalar matrix? Give one example. Also find $\left|\begin{array}{cc}4& 0\\ 0& 4\end{array}\right|$.

Let $A$ be a matrix of order $3\times 4$. If $R_1$ denotes the first row of $A$ and $C_2$ denotes its second column, then determine the orders of matrices $R_1$ and $C_2$.

Compute the indicated products.

$\left[\begin{array}{l}1\\ 2\\ 3\end{array}\right]\left[\begin{array}{lll}2& 3& 4\end{array}\right]$

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