# Write out the system of equations that corresponds to each of the following augmented matrices: (a)begin{pmatrix}3 & 2&|&8 1 & 5&|&7 end{pmatrix} (b)begin{pmatrix}5 & -2&1&|&3 2 & 3&-4&|&0 end{pmatrix} (c)begin{pmatrix}2 & 1&4&|&-1 4 & -2&3&|&4 5 & 2&6&|&-1 end{pmatrix} (d)begin{pmatrix}4 & -3&1&2&|&4 3 & 1&-5&6&|&5 1 & 1&2&4&|&85 & 1&3&-2&|&7 end{pmatrix}

Question
Matrices
Write out the system of equations that corresponds to each of the following augmented matrices:
(a)$$\begin{pmatrix}3 & 2&|&8 \\1 & 5&|&7 \end{pmatrix}$$
(b)$$\begin{pmatrix}5 & -2&1&|&3 \\2 & 3&-4&|&0 \end{pmatrix}$$
(c)$$\begin{pmatrix}2 & 1&4&|&-1 \\4 & -2&3&|&4 \\5 & 2&6&|&-1 \end{pmatrix}$$
(d)$$\begin{pmatrix}4 & -3&1&2&|&4 \\3 & 1&-5&6&|&5 \\1 & 1&2&4&|&8\\5 & 1&3&-2&|&7 \end{pmatrix}$$

2021-01-29
Step 1 Write out the system of equation to each of the following augmented matrices. Step 2 (a)$$\begin{bmatrix}3 & 2&|&8 \\1 & 5&|&7 \end{bmatrix}$$
In an augmented matrix, each row represents one equation of the system and each column represents a constant terms or variable.
When the columns represents the variables $$x_1 \text{ and } x_2$$
Hence, the system of equation of the given augmented matrix is $$\begin{cases}3x_1+2x_2=8\\x_1+5x_2=7\end{cases}$$
Step 3
(b)\begin{bmatrix}5 & -2&1&|&3 \\2 & 3&-4&|&0 \end{bmatrix}\)
In an augmented matrix, each row represents one equation of the system and each column represents a constant terms or variable.
When the columns represents the variables $$x_1 , x_2 \text{ and } x_3$$
Hence, the system of equation of the given augmented matrix is $$\begin{cases}5x_1-2x_2+x_3=3\\2x_1+3x_2-4x_3=0\end{cases}$$
Step 4
(c)\begin{bmatrix}2 & 1&4&|&-1 \\4 & -2&3&|&4 \\5 & 2&6&|&-1 \end{bmatrix}
In an augmented matrix, each row represents one equation of the system and each column represents a constant terms or variable.
When the columns represents the variables $$x_1 , x_2 \text{ and } x_3$$
Hence, the system of equation of the given augmented matrix is $$\begin{cases}2x_1+x_2+4x_3=-1\\4x_1-2x_2+3x_3=4\\5x_1+2x_2+6x_3=-1\end{cases}$$
Step 5
(d)$$\begin{bmatrix}4 & -3&1&2&|&4 \\3 & 1&-5&6&|&5 \\1 & 1&2&4&|&8\\5 & 1&3&-2&|&7 \end{bmatrix}$$
In an augmented matrix, each row represents one equation of the system and each column represents a constant terms or variable.
When the columns represents the variables $$x_1 , x_2 ,x_3 \text{ and } x_4$$
Hence, the system of equation of the given augmented matrix is $$\begin{cases}4x_1-3x_2+x_3+2x_4=4\\3x_1+x_2-5x_3+6x_4=5\\x_1+x_2+2x_3+4x_4=8\\5x_1+x_2+3x_3-2x_4=7\end{cases}$$

### Relevant Questions

Matrix multiplication is pretty tough- so i will cover that in class. In the meantime , compute the following if
$$A=\begin{bmatrix}2&1&1 \\-1&-1&4 \end{bmatrix} , B=\begin{bmatrix}0 & 2 \\-4 & 1\\2&-3 \end{bmatrix} , C=\begin{bmatrix}6 & -1 \\3 & 0\\-2&5 \end{bmatrix} , D=\begin{bmatrix}2 & -3&4 \\-3& 1&-2 \end{bmatrix}$$
If the operation is not possible , write NOT POSSIBLE and be able to explain why
a)A+B
b)B+C
c)2A
Determine the null space of each of the following matrices:
$$\begin{pmatrix}1 & 2 &-3&-1 \\ -2 & -4 & 6 &3 \end{pmatrix}$$
Let a linear sytem of equations Ax=b where
$$A=\begin{pmatrix}4 & 2&-2 \\2 & 2&-3\\-2&-3&14 \end{pmatrix} , b=\begin{pmatrix}10 , 5 , 4 \end{pmatrix}^T$$
in case we solve this equation system by using Dolittle LU factorization method , find Z and X matrices
Compute the following
a) \begin{bmatrix}-5 & -4&3&-10&-3&6 \\6&-10&5&9&4&-1 \end{bmatrix}+\begin{bmatrix}-7 & 3&10&0&8&8 \\8&0&4&-3&-8&0 \end{bmatrix}
b) -5\begin{bmatrix}8 & -10&7 \\0 & -9&7\\10&-5&-10\\1&5&-10 \end{bmatrix}
c)\begin{bmatrix}3 & 0&-8 \\6 & -4&-2\\6&0&-8\\-9&-7&-7 \end{bmatrix}^T
Find the product AB of the two matrices listed below:
$$A=\begin{pmatrix}2 & 1&3 \\-2 & 2&4\\-1&-3&-4 \end{pmatrix}$$
$$B=\begin{pmatrix}-1 & -2\\1 & 2\\3&4 \end{pmatrix}$$

Construct the augmented matrix that corresponds to the following system of equations.
$$\displaystyle{5}+\frac{{{8}{x}}}{{5}}={y}$$
$$2z−3(x−3y)=0$$
$$2x−y=3(x−4z)$$

$$A=\begin{bmatrix}2& 1&1 \\-1 & -1&4 \end{bmatrix} B=\begin{bmatrix}0& 2 \\-4 & 1\\2 & -3 \end{bmatrix} C=\begin{bmatrix}6& -1 \\3 & 0\\-2 & 5 \end{bmatrix} D=\begin{bmatrix}2& -3&4 \\-3 & 1&-2 \end{bmatrix}$$
a)$$A-3D$$
b)$$B+\frac{1}{2}$$
c) $$C+ \frac{1}{2}B$$
(a),(b),(c) need to be solved
$$A=\begin{bmatrix}2 & -3&7&-4 \\-11 & 2&6&7 \\6 & 0&2&7 \\5 & 1&5&-8 \end{bmatrix} B=\begin{bmatrix}3 & -1&2 \\0 & 1&4 \\3 & 2&1 \\-1 & 0&8 \end{bmatrix} , C=\begin{bmatrix}1& 0&3 &4&5 \end{bmatrix} , D =\begin{bmatrix}1\\ 3\\-2 \\0 \end{bmatrix}$$
$$\begin{pmatrix}1 & 3 &-4 \\ 2 & -1 & -1 \\ -1 & -3 &4 \end{pmatrix}$$
Let $$A=\begin{bmatrix}3 & 0 \\ -1 & 5 \end{bmatrix} , B=\begin{bmatrix}4 & -2 & 1 \\ 0 & 2 &3 \end{bmatrix} , C=\begin{bmatrix}1 & 2 \\ 3 & 4 \\ 5 &6 \end{bmatrix} , D=\begin{bmatrix}0 & -3 \\ -2 & 1 \end{bmatrix} , E=\begin{bmatrix}4 & 2 \end{bmatrix} , F=\begin{bmatrix}-1 \\ 2 \end{bmatrix}$$