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test whether equations 2x-3y+7z=5 3x+y-3z=13 2x+19y-47z=32 are consistent or not

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test whether equations 2x-3y+7z=5 3x+y-3z=13...

test whether equations 2x-3y+7z=5 3x+y-3z=13 2x+19y-47z=32 are consistent or not

solving equations

asked Feb 18, 2013 in Algebra 1 Answers by anonymous

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1 Answer

One way to test for consistency is to work out the determinant for the coefficients:

⎮ 2 -3 7 ⎟

⎮ 3 1 -3 ⎟= 2(-47+57)+3(-141+6)+7(57-2)=20-405+385=0.

⎮ 2 19 -47⎟

A zero determinant implies inconsistency. So the system is inconsistent.

answered Jul 18, 2022 by Rod Top Rated User (1.2m points)

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