How do you solve #24x + 24y + 16z = 106#, #8x + 24y + 40z = 135# and #24x + 16y - 8z = 42# using matrices?

1 Answer
Dec 16, 2017

Answer:

#x=11/8#, #y=13/8# and #z=17/8#

Explanation:

Perform the Gauss Jordan elimination on the augmented matrix

#A=((24,24,16,|,106),(8,24,40,|,135),(24,16,-8,|,42))#

I have written the equations not in the sequence as in the question in order to get #1# as pivot.

Perform the folowing operations on the rows of the matrix

#R1larrR1-3R2# ; #R3larrR3-3R2#

#A=((0,-48,-104,|,-299),(8,24,40,|,135),(0,-56,-128,|,-363))#

#R1larr(R1)/(-48)#

#A=((0,1,13/6,|,299/48),(8,24,40,|,135),(0,-56,-128,|,-363))#

#R2larrR1-24R1# ; #R3larrR3+56R1#

#A=((0,1,13/6,|,299/48),(8,0,-12,|,-29/2),(0,0,-20/3,|,-85/6))#

#R3larr(R3)*(-3/20)#

#A=((0,1,13/6,|,299/48),(8,0,-12,|,-29/2),(0,0,1,|,17/8))#

#R1larrR1-13/6R3# ; #R2larrR2+12R3#

#A=((0,1,0,|,13/8),(8,0,0,|,11),(0,0,1,|,17/8))#

#R2larr(R2)/8#

#A=((0,1,0,|,13/8),(1,0,0,|,11/8),(0,0,1,|,17/8))#

Thus, solution of equation system is #x=11/8#, #y=13/8# and #z=17/8#