Total number of solutions to the system of linear equations x + y + z = 1, 2x + 2y +2z = 3, x + y = 1 is .

0.0

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infinitely many

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non trivial

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Solution

The correct option is A 0.0
Once you express the given equations in the form of matrices the determinants are D = 0, $D_{1} = 1, D_{2} = - 1, D_{3} = 0$ . Therefore D = 0 and not all of $D_{1}, D_{2}, D_{3}$ are 0. So according to Cramer's rule there exists no solutions at all. So false.

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Total number of solutions to the system of linear equations $x + y + z = 1, 2 x + 2 y + 2 z = 3,$
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