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=4,3 x+2 y+5 z=3, 9 x+4 y+(28+[λ]) z=[λ] has a solution is:

Question

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=4,3 x+2 y+5 z=3, 9 x+4 y+(28+[λ]) z=[λ] has a solution is: (A) R (B) (-∞,-9) ∪(-9, ∞) (C) [-9,-8) (D) (-∞,-9) ∪[-8, ∞)

Tardigrade Admin · Accepted Answer

D =|1 1 1 3 2 5 9 4 28+[λ]|=-24-[λ]+15=-[λ]-9 if [λ]+9 ≠ 0 then unique solution if [λ]+9=0 then D 1= D 2= D 3=0 so infinite solutions Hence λ can be any red number.

Q. 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 $x + y + z = 4, 3 x + 2 y + 5 z = 3$ , $9 x + 4 y + (28 + [λ]) z = [λ]$ has a solution is:

$R$

$(- \infty, - 9) \cup (- 9, \infty)$

$[- 9, - 8)$

$(- \infty, - 9) \cup [- 8, \infty)$

$D = ∣ ∣ 139124 15 28 + [λ] ∣ ∣ = - 24 - [λ] + 15 = - [λ] - 9$
if $[λ] + 9 \neq = 0$ then unique solution
if $[λ] + 9 = 0$ then $D_{1} = D_{2} = D_{3} = 0$
so infinite solutions
Hence $λ$ can be any red number.

Q. 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:

R

(−∞,−9)∪(−9,∞)

[−9,−8)

(−∞,−9)∪[−8,∞)

D=∣∣​139​124​1528+[λ]​∣∣​=−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 λ can be any red number.

Q. 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 $x + y + z = 4, 3 x + 2 y + 5 z = 3$ , $9 x + 4 y + (28 + [λ]) z = [λ]$ has a solution is:

$R$

$(- \infty, - 9) \cup (- 9, \infty)$

$[- 9, - 8)$

$(- \infty, - 9) \cup [- 8, \infty)$

$D = ∣ ∣ 139124 15 28 + [λ] ∣ ∣ = - 24 - [λ] + 15 = - [λ] - 9$
if $[λ] + 9 \neq = 0$ then unique solution
if $[λ] + 9 = 0$ then $D_{1} = D_{2} = D_{3} = 0$
so infinite solutions
Hence $λ$ can be any red number.