Q2. - Algebra 2

Question

Give examples of a row matrix, a column matrix, a square matrix, and a zero matrix. State the dimension of each matrix.

Step-by-Step Solution

Answer

Following are the examples of a row matrix, a column matrix, a square matrix and a zero matrix and their dimensions respectively-

 

$\mathbf{A}\mathbf{=}\left[\begin{array}{ccc}\mathbf{1}& \mathbf{2}& \mathbf{3}\end{array}\right]$, dimension $\mathbf{1}\mathbf{\times }\mathbf{3}$

$\mathbf{A}\mathbf{=}\left[\begin{array}{c}\mathbf{1}\\ \mathbf{2}\\ \mathbf{3}\end{array}\right]$, dimension $\mathbf{3}\mathbf{\times }\mathbf{1}$

$\mathbf{A}\mathbf{=}\left[\begin{array}{cc}\mathbf{1}& \mathbf{2}\\ \mathbf{3}& \mathbf{4}\end{array}\right]$, dimension $\mathbf{2}\mathbf{\times }\mathbf{2}$

$\mathbf{A}\mathbf{=}\left[\begin{array}{cc}\mathbf{0}& \mathbf{0}\\ \mathbf{0}& \mathbf{0}\end{array}\right]$, dimension $\mathbf{2}\mathbf{\times }\mathbf{2}$

Step 1 – Example of a row matrix.

Give an example of row matrix and dimension of a matrix. 

$A=\left[\begin{array}{ccc}1& 2& 3\end{array}\right]$

The matrix $A$ has $1$ row and $3$ columns, the dimensions of matrix $A$ are $1\times 3$.

Step 2 – Example of a column matrix.

Give an example of column matrix and dimension of a matrix.

$A=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$

The matrix $A$ has $3$ rows and $1$ column, the dimensions of matrix $A$ are $3\times 1$.

Step 3 – Example of a square matrix.

Give an example of square matrix and dimension of a matrix.

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

The matrix $A$ has $2$ rows and $2$ columns, the dimensions of matrix $A$ are $2\times 2$.

Step 4 – Example of a zero matrix.

Give an example of zero matrix and dimension of a matrix.

$A=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$

The matrix $A$ has $2$ rows and $2$ columns, the dimensions of matrix $A$ are $2\times 2$.