# How do you solve 4p + 2q - 5r + 9s = -12, 2p + 6r - 7s = 0, 11q – 7r = -18, p + q - r + s = 1 using matrices?

Nov 6, 2016

[ (1,0,0,0,|,1141/145), (0,1,0,0,|,1636/145), (0,0,1,0,|,-2198/145), (0,0,0,1,|,-1558/145) ]

#### Explanation:

Here is the augmented matrix for the 4 equations:

[ (4,2,−5,9,|,−12), (2,0,6,−7,|,0), (0,11,–7, 0,|,−18), (1,1,-1,1,|,1) ]

The row operations required to resolve the above into an augmented identity matrix exceeds the limits placed on the length of an explanation. Here is the final matrix:

[ (1,0,0,0,|,1141/145), (0,1,0,0,|,1636/145), (0,0,1,0,|,-2198/145), (0,0,0,1,|,-1558/145) ]