### Video Transcript

Write the augmented matrix for the following system of equations: 𝑥 plus 𝑦 minus 𝑧 equals five, 𝑦 minus 𝑧 equals two, negative 𝑥 plus 𝑦 minus 𝑧 equals two.

We recall that if we have a general system of linear equations as shown, then the augmented matrix is made up of the coefficient matrix and the matrix of constants. In this question, since we have three equations and three variables, our coefficient matrix will be a three-by-three matrix. To complete the augmented matrix, we’ll then add the three constants. The coefficients of the first equation are one, one, and negative one. The second equation has no 𝑥-term, so the coefficients are zero, one, and negative one. Finally, the third equation has coefficients negative one, one, and negative one.

We can then add the three constants five, two, and two. The augmented matrix for the system of equations is one, one, negative one, five, zero, one, negative one, two, negative one, one, negative one, two. It is worth noting that for a system of linear equations with 𝑚 equations and 𝑛 variables, the augmented matrix has 𝑚 rows and 𝑛 plus one columns.