Question

pls help me its urgent ​

Answer 1

Step-by-step explanation:

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Answer 2

$\textsf{\large{\underline{Solution 1}:}}$

Here:

$\rm:\longmapsto A =\begin{bmatrix} 3&0\\ 0&-3\end{bmatrix}$

$\rm:\longmapsto B=\begin{bmatrix} 7&4\\ 2&5\end{bmatrix}$

Therefore, the matrix A + 2B will be:

$\rm=\begin{bmatrix} 3&0\\ 0&-3\end{bmatrix} + 2\begin{bmatrix} 7&4\\ 2&5\end{bmatrix}$

$\rm=\begin{bmatrix} 3&0\\ 0&-3\end{bmatrix} + \begin{bmatrix} 14&8\\ 4&10\end{bmatrix}$

$\rm= \begin{bmatrix} 17&8\\ 4&7\end{bmatrix}$

Therefore:

$\rm:\longmapsto A + 2 B=\begin{bmatrix} 17&8\\ 4&7\end{bmatrix}$

$\textsf{\large{\underline{Solution 2}:}}$

Here:

$\rm:\longmapsto A =\begin{bmatrix} 11&8\\ 2&5\end{bmatrix}$

$\rm:\longmapsto B=\begin{bmatrix} 12&3\\ 2&1\end{bmatrix}$

Therefore, the matrix B - A will be:

$\rm=\begin{bmatrix} 12&3\\ 2&1\end{bmatrix} - \begin{bmatrix} 11&8 \\ 2&5\end{bmatrix}$

$\rm=\begin{bmatrix} 1& - 5\\ 0& - 4\end{bmatrix}$

$\rm:\longmapsto B -A =\begin{bmatrix} 1& - 5\\ 0& - 4\end{bmatrix}$

$\textsf{\large{\underline{Solution 3}:}}$

Here:

$\rm:\longmapsto A =\begin{bmatrix} 1&0&0\\ 0&2&3 \\ 5&1&4\end{bmatrix}$

$\rm:\longmapsto B =\begin{bmatrix} 2&0&4\\ 5&1&3 \\ 1&7&3\end{bmatrix}$

Therefore, the matrix AB will be:

$\rm=\begin{bmatrix} 1&0&0\\ 0&2&3 \\ 5&1&4\end{bmatrix}\begin{bmatrix} 2&0&4\\ 5&1&3 \\ 1&7&3\end{bmatrix}$

$\rm=\begin{bmatrix} 2 + 0 + 0&0 + 0 + 0&4 + 0 + 0\\ 0 + 10 + 3&0 + 2 + 21&0 + 6 + 9 \\ 10 + 5 + 4&0 + 1 + 28&20 + 3 + 12\end{bmatrix}$

$\rm=\begin{bmatrix} 2&0 &4\\13& 23&15\\ 19&29&35\end{bmatrix}$

Therefore:

$\rm:\longmapsto AB = \begin{bmatrix} 2&0 &4\\13& 23&15\\ 19&29&35\end{bmatrix}$

$\textsf{\large{\underline{Solution 4}:}}$

Here:

$\rm:\longmapsto A =\begin{bmatrix} 1&4\\ 5&6\end{bmatrix}$

$\rm:\longmapsto B=\begin{bmatrix} 8&0\\ 2&4\end{bmatrix}$

Therefore, the matrix BA will be:

$\rm=\begin{bmatrix} 8&0\\ 2&4\end{bmatrix}\begin{bmatrix} 1&4 \\ 5&6\end{bmatrix}$

$\rm=\begin{bmatrix} 8 + 0&32 + 0\\ 2 + 20&8 + 24\end{bmatrix}$

$\rm=\begin{bmatrix} 8 &32\\ 22&32\end{bmatrix}$

Therefore:

$\rm: \longmapsto BA = \begin{bmatrix} 8 &32\\ 22&32\end{bmatrix}$

$\textsf{\large{\underline{Solution 5}:}}$

Here:

$\rm:\longmapsto A =\begin{bmatrix} 7&0\\ 3&5\end{bmatrix}$

$\rm:\longmapsto B=\begin{bmatrix} 3&0\\ 0&4 \end{bmatrix}$

Therefore, the matrix 3A - 4B will be:

$\rm = 3\begin{bmatrix} 7&0\\ 3&5\end{bmatrix} - 4\begin{bmatrix} 3&0 \\ 0&4\end{bmatrix}$

$\rm = \begin{bmatrix} 21&0\\ 9&15\end{bmatrix} - \begin{bmatrix} 12&0 \\ 0&16\end{bmatrix}$

$\rm = \begin{bmatrix} 9&0\\ 9& - 1\end{bmatrix}$

Therefore:

$\rm: \longmapsto 3A - 4B = \begin{bmatrix} 9&0\\ 9& - 1\end{bmatrix}$

$\textsf{\large{\underline{Learn More}:}}$

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:

$\rm:\longmapsto A=\begin{bmatrix}\rm 1&\rm 2&\rm 3\end{bmatrix}$

Column Matrix: This type of matrices have only 1 column. Example:

$\rm:\longmapsto A=\begin{bmatrix}\rm1\\ \rm2\\ \rm3\end{bmatrix}$

Square Matrix: In this type of matrix, number of rows and columns are equal. Example:

$\rm:\longmapsto A=\begin{bmatrix}\rm 1&\rm 2\\ \rm 3&\rm 4\end{bmatrix}$

Zero Matrix: It is a matrix with all elements present is zero. Example:

$\rm:\longmapsto A=\begin{bmatrix}\rm 0&\rm 0\\ \rm 0&\rm 0\end{bmatrix}$

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:

$\rm:\longmapsto A=\begin{bmatrix}\rm 1&\rm 0\\ \rm 0&\rm 1\end{bmatrix}$