Matrices and Determinants

JEE Main Mathematics · 17 questions

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• If the system of linear equations: x+y+z=6, x+2 y+5 z=10, 2 x+3 y+λ z=μ has infinitely many solutions, then the value of λ+μ…20268 April, Shift 2 · Q3
• Let A= [α, 1, 2; 2, 3, 0; 0, 4, 5] and B= [1, 0, 0; 0, -5 α, 0; 0, 4 α, -2 α] +adj(A). If det(B)=66, then det(adj(A)) equals:20268 April, Shift 2 · Q4
• 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
• Let A= [1, 0, 0; 3, 1, 0; 9, 3, 1] and B=[b_i j], 1 ≤ i, j ≤ 3. If B=A^99-I, then the value of (b_31-b_21)/(b_32) is:20266 April, Shift 2 · Q5
• Let A= [-1, 1, -1; 1, 0, 1; 0, 0, 1] satisfy A^2+α(adj(adj(A)))+β(adj(A)(adj(adj(A))))= [2, -2, 2; -2, 0, -1; 0, 0, -1] for some…20266 April, Shift 1 · Q21
• If f: N → Z is defined by f(n)= |n, -1, -5; -2 n^2, 3(2 k+1), 2 k+1; -3 n^3, 3 k(2 k+1), 3 k(k+2)+1|, k ∈ N, and Σ_n=1^k f(n)=98,…20265 April, Shift 2 · Q3
• Let M be a 3 × 3 matrix such that M (1; 0; 0) = (1; 2; 3), M (0; 1; 0) = (0; 1; 2) and M (0; 0; 1) = (-1; 1; 1). If M (x; y; z) =…20265 April, Shift 2 · Q4
• Let A be a 3 × 3 matrix such that A^T [1; 0; 1] = [5; 2; 2], A^T [0; 0; 1] = [3; 1; 1], A [1; 0; 1] = [3; 4; 4] and A [0; 0; 1] =…20265 April, Shift 1 · Q3
• 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
• If the system of equations: x+y+z=5; x+2 y+3 z=9; x+3 y+λ z=μ has infinitely many solutions, then the value of λ+μ is:20264 April, Shift 2 · Q3
• Let A= [1, 2, 7; 4, -2, 8; 3, 8, -7] and det(A-α I)=0, where α is a real number. If the largest possible value of α is p, then…20264 April, Shift 2 · Q6
• Let S={A= [a, b; c, d]: a, b, c, d ∈{0,1,2,3,4}. and.A^2-4 A+3 I=0} be a set of 2 × 2 matrices. Then the number of matrices in S,…20264 April, Shift 1 · Q5
• Let A= [1, 1, 2; -2, 0, 1; 1, 3, 5]. Then the sum of all elements of the matrix adj(adj(2(adj A)^-1)) is equal to:20264 April, Shift 1 · Q6
• If the system of equations x+5 y+6 z=4, 2 x+3 y+4 z=7, x+6 y+a z=b has infinitely many solutions, then the point (a, b) lies on…20262 April, Shift 2 · Q3
• Consider the matrices A= [2, -2; 4, -2] and B= [3, 9; 1, 3]. If matrices P and Q are such that PA=B and A Q=B, then the absolute…20262 April, Shift 2 · Q22
• Let α, β ∈ R be such that the system of linear equations x+2 y+z=5; 2 x+y+α z=5; 8 x+4 y+β z=18 has no solution. Then (β)/(α) is…20262 April, Shift 1 · Q3
• Let A= [1, 2; 1, α] and B= [3, 3; β, 2]. If A^2-4 A+I=O and B^2-5 B-6 I=O, then among the two statements: (S1): [(B-A)(B+A)]^T=…20262 April, Shift 1 · Q4