How do you solve a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9 using matrices?

1 Answer
Jan 19, 2018

a=2, b=-3 and c=5

Explanation:

Perform the Gauss Jordan elimination on the augmented matrix

A=((1,3,2,|,3),(2,-1,-3,|,-8),(5,2,1,|,9))

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

R2larrR2-2R1; R3larrR3-5R1

A=((1,3,2,|,3),(0,-7,-7,|,-14),(0,-13,-9,|,-6))

R2larr(R2)/(-7)

A=((1,3,2,|,3),(0,1,1,|,2),(0,-13,-9,|,-6))

R3larrR3+13R2

A=((1,3,2,|,3),(0,1,1,|,2),(0,0,4,|,20))

R3larr(R3)/4

A=((1,3,2,|,3),(0,1,1,|,2),(0,0,1,|,5))

R1larrR1-2R3; R2larrR2-R3

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

R1larrR1-3R2

A=((1,0,0,|,2),(0,1,0,|,-3),(0,0,1,|,5))

Thus a=2, b=-3 and c=5