Step-by-step explanation:
[tex]\textsf{\large{\underline{Solution 1}:}}[/tex]
Here:
[tex]\rm:\longmapsto A =\begin{bmatrix} 3&0\\ 0&-3\end{bmatrix}[/tex]
[tex]\rm:\longmapsto B=\begin{bmatrix} 7&4\\ 2&5\end{bmatrix}[/tex]
Therefore, the matrix A + 2B will be:
[tex]\rm=\begin{bmatrix} 3&0\\ 0&-3\end{bmatrix} + 2\begin{bmatrix} 7&4\\ 2&5\end{bmatrix} [/tex]
[tex]\rm=\begin{bmatrix} 3&0\\ 0&-3\end{bmatrix} + \begin{bmatrix} 14&8\\ 4&10\end{bmatrix} [/tex]
[tex]\rm= \begin{bmatrix} 17&8\\ 4&7\end{bmatrix} [/tex]
Therefore:
[tex]\rm:\longmapsto A + 2 B=\begin{bmatrix} 17&8\\ 4&7\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]
