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}

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
asked 2021-01-28
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)\(\begin{pmatrix}4 & -3&1&2&|&4 \\3 & 1&-5&6&|&5 \\1 & 1&2&4&|&8\\5 & 1&3&-2&|&7 \end{pmatrix}\)

Answers (1)

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 \(\begin{cases}4x_1-3x_2+x_3+2x_4=4\\3x_1+x_2-5x_3+6x_4=5\\x_1+x_2+2x_3+4x_4=8\\5x_1+x_2+3x_3-2x_4=7\end{cases}\)
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