Solve the following system of linear equations by Cramers rule: `x+y+z+1=0,\ \ a x+b y+c z+d=0,\ \ a^2x+b^2y+c^2z+d^2=0`

Explanation

We have given:`x+y+z+1=0,\ \ a x+b y+c z+d=0,\ \ a^2x+b^2y+c^2z+d^2=0`

As we know that the system of linear equation can be written in matrix form as `AX = B`

`implies A=|(1,1,1),(a,b,c),(a^2,b^2,c^2)|`,`X=[(x),(y),(z)]`,`B=[(-1),(-d),(-d^2)]`

Now find the determinant of `A`,

`|A|= |(1,1,1),(a,b,c),(a^2,b^2,c^2)|`

Now apply `C_2->C_2-C_1,C_3->C_3-C_1`

`|A|=|(1,0,0),(a,b-a,c-a),(a^2,b^2-a^2,c^2-a^2)|`

Then

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