Answer:
[tex]\textsf{\large{\underline{Solution 3}:}}[/tex]
Here:
[tex]\rm:\longmapsto A =\begin{bmatrix} 1&0&0\\ 0&2&3 \\ 5&1&4\end{bmatrix}[/tex]
[tex]\rm:\longmapsto B =\begin{bmatrix} 2&0&4\\ 5&1&3 \\ 1&7&3\end{bmatrix}[/tex]
Therefore, the matrix AB will be:
[tex]\rm=\begin{bmatrix} 1&0&0\\ 0&2&3 \\ 5&1&4\end{bmatrix}\begin{bmatrix} 2&0&4\\ 5&1&3 \\ 1&7&3\end{bmatrix}[/tex]
[tex]\rm=\begin{bmatrix} 2 + 0 + 0&0 + 0 + 0&4 + 0 + 0\\ 0 + 10 + 3&0 + 2 + 21&0 + 6 + 9 \\ 10 + 5 + 4&0 + 1 + 28&20 + 3 + 12\end{bmatrix}[/tex]
[tex]\rm=\begin{bmatrix} 2&0 &4\\13& 23&15\\ 19&29&35\end{bmatrix}[/tex]
Therefore:
[tex]\rm:\longmapsto AB = \begin{bmatrix} 2&0 &4\\13& 23&15\\ 19&29&35\end{bmatrix}[/tex]
[tex]\textsf{\large{\underline{Learn More}:}}[/tex]
Matrix: A matrix is a rectangular arrangement of numbers in the form of horizontal and vertical lines.
Horizontal lines are called rows and vertical lines are called columns.
Order of Matrix:
A matrix containing x rows and y column has order x × y and it has xy elements.
Different types of matrices:
Row Matrix: This type of matrices have only 1 row. Example:
[tex]\rm:\longmapsto A=\begin{bmatrix}\rm 1&\rm 2&\rm 3\end{bmatrix}[/tex]
Column Matrix: This type of matrices have only 1 column. Example:
[tex]\rm:\longmapsto A=\begin{bmatrix}\rm1\\ \rm2\\ \rm3\end{bmatrix}[/tex]
Square Matrix: In this type of matrix, number of rows and columns are equal. Example:
[tex]\rm:\longmapsto A=\begin{bmatrix}\rm 1&\rm 2\\ \rm 3&\rm 4\end{bmatrix}[/tex]
Zero Matrix: It is a matrix with all elements present is zero. Example:
[tex]\rm:\longmapsto A=\begin{bmatrix}\rm 0&\rm 0\\ \rm 0&\rm 0\end{bmatrix}[/tex]
Identity Matrix: In this type of matrix, diagonal element is 1 and remaining elements are zero. An Identity matrix is always a square matrix. Example:
[tex]\rm:\longmapsto A=\begin{bmatrix}\rm 1&\rm 0\\ \rm 0&\rm 1\end{bmatrix}[/tex]
