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Matrices and Determinants question

2023 · 31 Jan · Shift 1 · Q29

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JEE Main
Mathematics
Matrices and Determinants
2023 · 31 Jan · Shift 1 · Q29

Matrices and Determinants question

2023 · 31 Jan · Shift 1 · Q29

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

For the system of linear equations

x+y+z=6\alpha x+\beta y+7 z=3x+2 y+3 z=14

which of the following is NOT true ?

A
If $\alpha=\beta=7$ , then the system has no solution
B
For every point $(\alpha, \beta) eq(7,7)$ on the line $x-2 y+7=0$ , the system has infinitely many solutions
C
There is a unique point $(\alpha, \beta)$ on the line $x+2 y+18=0$ for which the system has infinitely many solutions
D
If $\alpha=\beta$ and $\alpha eq 7$ , then the system has a unique solution

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