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

1 Answer
Nov 6, 2016

Answer:

#[ (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) ]#