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16/01/2022 5:39 pm
Topic starter
Let [λ] be the greatest integer less than or equal to λ. The set of all values of λ for which the system of linear equations x + y + z = 4, 3x + 2y+ 5z = 3, 9x + 4y + (28+ [λ])z = [λ] has a solution is:
(1) R
(2) (-∞, 9) ∪ (-9, ∞)
(3) [–9, –8)
(4) (-∞, -9) ∪ [-8, ∞)
1 Answer
1
16/01/2022 5:43 pm
Correct answer: (1) R
Explanation:
D = \(\begin{vmatrix} 1 & 1 & 1 \\[0.3em] 3 & 2 & 5 \\[0.3em] 9 & 4 & 28+[λ] \end{vmatrix}\)
= -24 - [λ] + 15 = -[λ] - 9
if [λ] + 9 ≠ 0 then unique solution
if [λ] + 9 = 0 then D1 = D2 = D3 = 0
so infinite solutions
Hence l can be any red number.