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

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

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How do you solve -x + y + z = -1−x+y+z=−1-x + y + z = -1 and -x + 5y - 15z = -13−x+5y−15z=−13-x + 5y - 15z = -13 and 3x - 2y - 7z = 03x−2y−7z=03x - 2y - 7z = 0 using matrices?

1 Answer

Explanation:

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