Matrices and determinants

The values of Î± for which the system of equations x+y+z=1
x+4y+10z=Î±². x+2y+4z=Î±....is consistent are given by..
Ans.(1.2)

2 Answers

x+y+z=1
x+4y+10z=Î±²
x+2y+4z=Î±.

from the first 2, we get 3y+9z=a²-1

from the 2 and 3, we get y+3z=a-1

now for consistency we have to have this that

(a²-1)=3(a-1)

hence a=1 or a=2

Sir..Is this the general method for solving such type of problems?
And what is meant by consistency?

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