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

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Answer 1 · 2018-02-02T10:57:11

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

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 $t=7$

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