Question

- 6x - 3y + 5z = 7 15x – 3y - 72 = 13 5x +15y + 5z = - 8 a.) Write the systems of equations as a matrix.

Answer 1

`\left[\begin{array}ccc -6 & -3 & 5 & 7\\15 & -3 & -72 & 13\\5 & 15 & 5 & -8\\\end{array}\right]`

Step-by-step explanation

The coefficients of the left hand side of -6x-3y+5z = 7 are -6, -3, and 5. They correspond to variables x, y, and z in that order.

The coefficients -6, -3, 5 will then go along the first 3 slots of row 1. Refer to the matrix shown above. The last slot of row 1 is the value 7, which is the value on the right hand side of the equation -6x-3y+5z = 7.

The other rows are filled out in the same fashion. The vertical bar is there to separate the coefficients on the left hand side vs the right hand side values. Some teachers and textbooks will leave out the vertical bar.

Side note: This augmented matrix is of size 3x4 since it has 3 rows and 4 columns.