How do you solve #-x + y + z = -1# and #-x + 5y - 15z = -13# and #3x - 2y - 7z = 0# using matrices?

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How do you solve #-x + y + z = -1# and #-x + 5y - 15z = -13# and #3x - 2y - 7z = 0# using matrices?

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Answer 1 · 2016-02-22T22:03:40

This is a impossible system of equations and has no solution.

Explanation:

#Delta=[[-1,1,1],[-1,5, -15],[3,-2,-7]]=35-45+2-(15-30+7)=-8+8=0#
#Delta x=[[-1,1,1],[-13,5, -15],[0,-2,-7]]=35+0+26-(0-30+91)=61-61=0#
#Delta y=[[-1,-1,1],[-1,-13, -15],[3,0,-7]]=-91+45+0-(-39-7+0)=-46+46=0#
#Delta z=[[-1,1,-1],[-1,5, -13],[3,-2,0]]=0-39-2-(15-26+0)=-41+11=-10#

Since #Delta =0# but #Delta z !=0# this system of equations is a impossible one and has no solution.

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How do you solve #-x + y + z = -1# and #-x + 5y - 15z = -13# and #3x - 2y - 7z = 0# using matrices?

1 Answer

Explanation:

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