Basics of Matrices

$A$ is square matrix of order '$n$'.

$\ell =$ maximum number of distinct entries if '$A$' is a triangular matrix

$m=$ maximum number of distinct entries if '$A$' is a diagonal matrix

$p=$ minimum number of zeroes if '$A$' is a triangular matrix

If $\mathrm{ \ell }+5=p+2m$, find the order of the matrix.

A matrix, in which number of rows is less than the number of columns, is called 

A triangular matrix $A={\left[a_{ij}\right]}_{n\times n}$ is said to be a diagonal matrix if $a_{\mathit{i}\mathit{j}}=0$ for

If a vertical matrix has $2$ rows then the number of columns can be:

 Is the matrix given below is Horizontal Matrix ? (give answer as Yes or No)

$\left[\begin{array}{ccc}5& 0& 1\\ 3& 2& 4\\ 0& 5& 1\end{array}\right]$

If a vertical matrix has $4$ rows then the number of columns can be:

If a horizontal matrix has $4$ rows then the number of columns can be:

If $A=\left[\begin{array}{c}2\\ 1\end{array}\right], B=\left[\begin{array}{c}2\\ -1\end{array}\right]$ and $C=\left[\begin{array}{c}0\\ -8\end{array}\right]$, then $A+B+C$ is a:

If $A=\left[\begin{array}{ccc}x& y& u\\ z& w& v\end{array} \right], B=\left[\begin{array}{ccc}x& -y& u\\ -z& w& -v\end{array} \right]$ then $A+B$ is a:

State the type of the following matrix:

$\left[\begin{array}{c}3\\ 2\end{array}\right]$

State the type of the following matrix:

$\left[\begin{array}{ccc}2& 3& 2\end{array}\right]$

State the type of the following matrix:

$\left[\begin{array}{cc}1& 0\\ 2& 3\\ 4& 5\end{array}\right]$

State the type of the following matrix:

$\left[\begin{array}{ccc}2& 0& 0\\ 0& 2& 0\end{array}\right]$

Find the number of submatrices of matrix $\left[\begin{array}{cc}1& 2\\ 5& 6\\ 7& 8\end{array}\right]$.

Find the number of submatrices of matrix $\left[\begin{array}{ccc}1& 5& 6\end{array}\right]$.

Find the number of submatrices of matrix $\left[\begin{array}{cc}1& 2\\ 5& 6\end{array}\right]$.

Find the number of submatrices of matrix $\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\end{array}\right]$.

Wihch of the following is a diagonal matrix.