[tex]\textsf{\large{\underline{Solution 5}:}}[/tex]
Here:
[tex]\rm:\longmapsto A =\begin{bmatrix} 7&0\\ 3&5\end{bmatrix}[/tex]
[tex]\rm:\longmapsto B=\begin{bmatrix} 3&0\\ 0&4 \end{bmatrix}[/tex]
Therefore, the matrix 3A - 4B will be:
[tex]\rm = 3\begin{bmatrix} 7&0\\ 3&5\end{bmatrix} - 4\begin{bmatrix} 3&0 \\ 0&4\end{bmatrix}[/tex]
[tex]\rm = \begin{bmatrix} 21&0\\ 9&15\end{bmatrix} - \begin{bmatrix} 12&0 \\ 0&16\end{bmatrix}[/tex]
[tex]\rm = \begin{bmatrix} 9&0\\ 9& - 1\end{bmatrix} [/tex]
Therefore:
[tex]\rm: \longmapsto 3A - 4B = \begin{bmatrix} 9&0\\ 9& - 1\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]
