Homogeneous System of Linear Equations

JEE Main Mathematics · Matrices and Determinants · 6 questions, latest first

• The sum of all possible values of θ ∈[0,2 π], for which the system of equations: x cos 3 θ-8 y-12 z=0; x cos 2 θ+3 y+3 z=0; x+y+3…20266 April, Shift 2 · Q4
• Consider the system of linear equations in x, y, z: x+2 y+t z=0, 6 x+y+5 t z=0, 3 x+t^2 y+f(t) z=0, where f: R → R is a…20265 April, Shift 1 · Q4
• Let α β γ=45; α, β, γ ∈ R. If x(α, 1,2)+y(1, β, 2)+z(2,3, γ)=(0,0,0) for some x, y, z ∈ R, x y z ≠ 0, then 6 α+4 β+γ is equal to…20246 April, Shift 1 · Q22
• If the system of equations x+(√2 sin α) y+(√2 cos α) z=0; x+( cos α) y+( sin α) z=0; x+( sin α) y-( cos α) z=0 has a non-trivial…20244 April, Shift 1 · Q4
• Let S be the set of all values of θ ∈[-π, π] for which the system of linear equations x+y+√3 z=0; -x+( tan θ) y+√7 z=0; x+y+( tan…20238 April, Shift 2 · Q3
• If a point P(α, β, γ) satisfying (α β γ) (2, 10, 8; 9, 3, 8; 8, 4, 8) = (0, 0, 0) lies on the plane 2 x+4 y+3 z=5, then 6 α+9 β+7…202331 January, Shift 2 · Q64