Matrices & DeterminantsmediumPYQ · JEE Main · 4 Apr 2026 · Shift 2 (Afternoon)Free

Infinitely Many Solutions: λ + μ = 18 | JEE Main 2026

JEE Maths question with a full step-by-step solution.

Question
If the system of equations x+y+z=5, x+2y+3z=9, x+3y+λz=μx+y+z=5,\ x+2y+3z=9,\ x+3y+\lambda z=\mu has infinitely many solutions, then the value of λ+μ\lambda+\mu is
A1616
B1818correct
C1919
D2121
Solution
Step 1: Compute the determinants (with DD = coefficient determinant):
D=λ−5,D1=λ+μ−18,D2=4λ−2μ+6,D3=μ−13.D=\lambda-5,\quad D_1=\lambda+\mu-18,\quad D_2=4\lambda-2\mu+6,\quad D_3=\mu-13.
 Step 2: For infinitely many solutions, D=D1=D2=D3=0D=D_1=D_2=D_3=0. Step 3: D=0⇒λ=5D=0\Rightarrow\lambda=5; D3=0⇒μ=13D_3=0\Rightarrow\mu=13. (These also make D1D_1 and D2D_2 zero.) Step 4:
λ+μ=5+13=18.\lambda+\mu=5+13=18.
 Correct answer: (2)
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