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MathsMediumMCQ2019 Β· 09 Jan Shift 1

Q77.The system of linear equations π‘₯+ 𝑦+ 𝑧= 2 2π‘₯+ 3𝑦+ 2𝑧= 5 2π‘₯+ 3𝑦+ π‘Ž2 - 1𝑧= π‘Ž+ 1 (1) is inconsistent when π‘Ž= √3 (2) has a unique solution for π‘Ž= √3 (3) has infinitely many solutions for π‘Ž= 4 (4) is inconsistent when π‘Ž= 4

What This Question Tests

This problem tests the conditions for a system of linear equations to have a unique solution, no solution (inconsistent), or infinitely many solutions, primarily using the determinant of the coefficient matrix.

Concepts Tested

Consistent/inconsistent systemUnique solutionNo solutionInfinitely many solutionsDeterminants

Formulas Used

Determinant of coefficient matrix for solution types (Cramer's Rule related concepts)

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