From the following matrices, identify (a) Square matrices (b) Rectangular matrices (c) Row matrices (d) Column matrices (e) Identity matrices (f) Null matrices | ClassNotes

Aug 01, 2022

Question:

From the following matrices, identify

(a) Square matrices	(b) Rectangular matrices	(c) Row matrices
(d) Column matrices	(e) Identity matrices	(f) Null matrices

(i) $\left[ \begin{matrix} -8 & 2 & 7 \\ 12 & 0 & 4 \\ \end{matrix} \right]$	(ii) $~\left[ \begin{matrix} 3 \\ 0 \\ 1 \\ \end{matrix} \right]$
(iii) $\left[ \begin{matrix} 6 & -4 \\ 3 & -2 \\ \end{matrix} \right]$	(iv) $\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]$
(v) $\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \\ \end{matrix} \right]$	(vi) $\left[ 3~~~~~~10~~~~-1 \right]$
(vii) $\left[ \begin{matrix} 1 \\ 0 \\ 0 \\ \end{matrix} \right]$	(viii) $\left[ \begin{matrix} 1 & 2 & 3 \\ -1 & 2 & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right]$
(ix) $\left[ \begin{matrix} 0 & 0 \\ 0 & 0 \\ 0 & 0 \\ \end{matrix} \right]$

Difficulty: Easy

Solution:

(a) (iii), (iv) and (viii) are square matrices because the number of rows are equal to number of columns.

(b) (i), (ii), (v), (vi) (vii), (ix) are rectangular matrices because their rows and columns are not equal.

(c) (vi) is a row matrix because it has only one row.

(d) (ii) and (vii) are column matrices because they have only one column.

(e) (iv) is an identity matrix as well because its diagonal elements are $1$ and all non-diagonal elements are $0$.

(f) (ix) is a null matrix because its each entry is zero.