Write the system of equations as an augmented matrix

⎧⎪⎨⎪⎩u=150−7s+4m=25019s−11m=300

Your equations are mangled, but this web site will show the operations in detail:

http://matrix.reshish.com/gauss-jordanElimination.php

To write the system of equations as an augmented matrix, we can arrange the coefficients of the variables and the constants in a matrix format.

The given system of equations is:

u = 150 - 7s + 4m ...(1)
19s - 11m = 300 ...(2)

We can write the system of equations as an augmented matrix [A | B] as follows:

⎡ 0 -7 4 | 150 ⎤
⎢ ⎥
⎣ 19 -11 0 | 300 ⎦

In this augmented matrix, the left side represents the coefficients of the variables (u, s, and m), and the right side represents the constants (150 and 300).

To write the system of equations as an augmented matrix, we will place the coefficients and the constants of the variables in a matrix form with the right-hand sides of the equations in the last column.

The system of equations is:

⎧⎪⎨⎪⎩u = 150 − 7s + 4m = 250
19s − 11m = 300

We can rewrite the equations in the form Ax = b, where A is the matrix of coefficients, x is the column vector of variables, and b is the column vector of constants.

The matrix A is formed by the coefficients of the variables u, s, and m:

A = [1 -7 4]
[0 19 -11]

The column vector x is formed by the variables u, s, and m:

x = [u]
[s]
[m]

The column vector b is formed by the constants 150, 250, and 300:

b = [150]
[250]
[300]

Now, we can combine A, x, and b into an augmented matrix:

[A | b] = [1 -7 4 | 150]
[0 19 -11 | 250]
[0 0 0 | 300]

So, the augmented matrix representation of the system of equations is:

⎡ 1 -7 4 | 150 ⎤
⎢ ⎥
⎢ 0 19 -11 | 250 ⎥
⎢ ⎥
⎣ 0 0 0 | 300 ⎦