How do you solve the system #2a+b=3, 5a=15, a+b+c=-1# using matrices?

1 Answer
Oct 23, 2016

Answer:

Please see the explanation for the procedure.

Explanation:

Write #5a = 15# into the first row of the augmented matrix:

#[ (5, 0,0,|,15) ]#

Add the row for #2a + b = 3#:

#[ (5, 0,0,|,15), (2, 1, 0,|,3) ]#

Add the row for #a + b + c = -1#:

#[ (5, 0,0,|,15), (2, 1, 0,|,3), (1,1,1,|,-1) ]#

Divide the first row by 5:

#[ (1, 0,0,|,3), (2, 1, 0,|,3), (1,1,1,|,-1) ]#

Multiply the first row by -2 and then add to row 2:

#[ (1, 0,0,|,3), (0, 1, 0,|,-3), (1,1,1,|,-1) ]#

Subtract row 1 from the row 3:

#[ (1, 0,0,|,3), (0, 1, 0,|,-3), (0,1,1,|,-4) ]#

Subtract row 2 from row 3:

#[ (1, 0,0,|,3), (0, 1, 0,|,-3), (0,0,1,|,-1) ]#

#a = 3, b = -3, c = -1#

Check:

#2(3) + -3 = 3#
#5(3) = 15#
#3 + -3 + -1 = -1#

#3 = 3#
#15 = 15#
#-1 = -1#

This checks