How do you solve the system #r+s+t=15, r+t=12, s+t=10# using matrices?

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Answer 1 · 2018-02-02T10:57:11

#r=5#, #s=3# and #t=7#

Perform the Gauss Jordan elimination on the augmented matrix

#A=((1,1,1,|,15),(1,0,1,|,12),(0,1,1,|,10))#

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

#R2larrR2-R1#

#A=((1,1,1,|,15),(0,-1,-0,|,-3),(0,1,1,|,10))#

#R1larrR1+R2#; #R3larrR3+R2#

#A=((1,0,1,|,12),(0,-1,-0,|,-3),(0,0,1,|,7))#

#R1larrR1-R3#

#A=((1,0,0,|,5),(0,-1,-0,|,-3),(0,0,1,|,7))#

#R2larr(R2)*(-1)#

#A=((1,0,0,|,5),(0,1,0,|,3),(0,0,1,|,7))#

Thus #r=5#, #s=3# and #t=7#