Gaussian elimination problem

Question

$$x_1 + 10x_2 − 3x_3 = 8$$

$$x_1 + 10x_2 + 2x_3 = 13$$

$$x_1 + 4x_2 + 2x_3 = 7$$

when making 2nd and 3rd 1st columns 0 using Gaussian elimination, the second row second column also becomes zero, so then i cant have a diagonal set of ones in the matrix. What do?

Thanks in advance, i appreciate your intelligence.

Answer 1

After getting $$\pmatrix{1&10&-3\\0&0&5\\0&-6&5}$$ , simply swap the second and the third row and continute the algorithm.