Question

Define : 

(i) Row Matrix 

(ii) Column Matrix 

(iii) Squre Matrix 

(iv) Zero Matrix 

(v) Diagonal Marix 

(vi) Unit Marix

Answer 1

(i) Row Matrix : A matrix having only one row is called a row matrix. 

For example, A = [ 4 1] is a row matrix of order 1 × 2 (1 row, 2 columns) 

B = [ 5 –1 \(\frac12\) ] is a row matrix of order 1 × 3.

(ii) Column Matrix : A matrix having only one column is called a column matrix. 

For example, A = \(\begin{bmatrix} 1 \\[0.1em] 2\end{bmatrix}\) is a column matrix of order 2 × 1 ( 2 rows, 1 column) 

B = \(\begin{bmatrix} -1 \\[0.1em] 4 \\[0.3em] 5 \\[0.3em] 3 \end{bmatrix}\) is a column matrix of order 4 × 1.

(iii) Square Matrix : A matrix having the same number of columns as it has rows is called a square matrix. 

For example, A =  \(\begin{bmatrix} 4 & 7 \\[0.1em] -2 & 9\end{bmatrix}\) having 2 rows and 2 columns is 2 × 2 square matrix or a square matrix of order 2. It may also be denoted by A₂ . 

B₃ = \(\begin{bmatrix} 1 & 4 & 9 \\[0.1em] 2 & -4 & 5 \\[0.3em] -3&4&8\end{bmatrix}\)is a square matrix of order 3

(iv) Zero Matrix : A matrix each of whose elements is zero is called a zero matrix or null matrix. 

For example,   0₂ = \(\begin{bmatrix} 0& 0 \\[0.1em] 0 & 0\end{bmatrix},\) 0_2x4 = \(\begin{bmatrix} 0& 0&0&0 \\[0.1em] 0 & 0&0&0\end{bmatrix}\)

(v) Diagonal Matrix : A square matrix having all the elements zero, except the principal diagonal elements is called a diagonal matrix. 

For example, 

(vi) Unit Matrix : A square matrix in which each diagonal element is unity, all other elements being zero, is called a Unit matrix or Identity matrix.

I₂ = \(\begin{bmatrix} 1 & 0 \\[0.1em] 0 & 1\end{bmatrix},\) I₃ = \(\begin{bmatrix} 1 & 0 & 0 \\[0.1em] 0 & 1 & 0 \\[0.3em] 0&0&1\end{bmatrix}\)