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Matrices and Determinants question

2023 · 1 Feb · Shift 2 · Q28

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JEE Main
Mathematics
Matrices and Determinants
2023 · 1 Feb · Shift 2 · Q28

Matrices and Determinants question

2023 · 1 Feb · Shift 2 · Q28

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

For the system of linear equations

\alpha x+y+z=1,x+\alpha y+z=1,x+y+\alpha z=\beta

, which one of the following statements is NOT correct?

A
It has infinitely many solutions if $\alpha=1$ and $\beta=1$
B
It has infinitely many solutions if $\alpha=2$ and $\beta=-1$
C
$x+y+z=\frac{3}{4}$ if $\alpha=2$ and $\beta=1$
D
It has no solution if $\alpha=-2$ and $\beta=1$

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