Questions: Write the system of equations as an augmented matrix 6 n -8 n+u r=100 n+7 r n [ ]

Solution Steps

To write the given system of equations as an augmented matrix, we first need to express each equation in the standard form \( ax + by + cz = d \). Then, we can extract the coefficients of the variables and the constants to form the augmented matrix. The system of equations provided seems incomplete or incorrectly formatted, so I'll assume a typical form for illustration purposes.

1. Identify the coefficients of each variable in the equations.
2. Arrange these coefficients into rows of a matrix, with each row representing an equation.
3. The constants on the right side of the equations form the last column of the augmented matrix.

We start with the following system of equations based on the provided information:

1. \( 6n = 0 \)
2. \( -8n + ur = 100 \)
3. \( n + 7r = 0 \)
4. \( n = 0 \)

From these equations, we can extract the coefficients for each variable \( n \), \( u \), and \( r \) along with the constants on the right side. The coefficients can be summarized as follows:

• For the first equation: \( [6, 0, 0] \) with constant \( 0 \)
• For the second equation: \( [-8, 1, 0] \) with constant \( 100 \)
• For the third equation: \( [1, 0, 7] \) with constant \( 0 \)
• For the fourth equation: \( [1, 0, 0] \) with constant \( 0 \)

The augmented matrix representing the system of equations is constructed by combining the coefficients and constants: \[ \begin{bmatrix} 6 & 0 & 0 & 0 \\ -8 & 1 & 0 & 100 \\ 1 & 0 & 7 & 0 \\ 1 & 0 & 0 & 0 \end{bmatrix} \]

Final Answer