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Using matrix method, show that following...

Using matrix method, show that following system of equation is inconsistent : `2x+3y-z+4=0` `x-y+2z-7=0` `x+4y-3z+5=0`

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The given system of equation is
`underset(A)([(2,3,-1),(1,-1,2),(1,4,-3)])underset(X)([(x),(y),(z)])=underset(B)([(-4),(7),(-5)])`
`|A|=|(2,3,-1),(1,-1,2),(1,4,-3)|=0`
Also, (adj. A) `B=[(-5,5,5),(5,-5,-5),(5,-5,-5)][(-4),(7),(-5)]=[(30),(-30),(-30)] ne O`
thus, system is inconsistent.
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