Matrices questions
472 published questions with worked solutions.
- Let a,b,c be positive numbers. The following system of equations in x,y and z: x^2 a^2 + y^2 b^2 - z^2 c^2 =1; x^2 a^2 - y^2 b^2...
- If the system of equations x + 5y + 6z = 4, 2x + 3y + 4z = 7, x + 6y + az = b has infinitely many solutions, then the point (a,...
- Consider the matrices A = bmatrix 2 & -2 4 & -2 bmatrix and B = bmatrix 3 & 9 1 & 3 bmatrix . If matrices P and Q are such that...
- Let α, β ∈ ℝ be such that the system of linear equations x + 2y + z = 5, 2x + y + αz = 5, 8x + 4y + βz = 18 has no solution. Then...
- Let A = bmatrix 1 & 2 1 & bmatrix and B = bmatrix 3 & 3 & 2 bmatrix . If A² − 4A + I = O and B² − 5B − 6I = O, then among the two...
- Let S = A = bmatrix a & b c & d bmatrix : a,b,c,d 0,1,2,3,4 and A^2 - 4A + 3I = 0 be a set of 2 × 2 matrices. Then the number of...
- Let A = bmatrix 1 & 1 & 2 -2 & 0 & 1 1 & 3 & 5 bmatrix . Then the sum of all elements of the matrix adj(adj(2(adjA)⁻¹)) is equal...
- If the system of equations x+y+z=5, x+2y+3z=9, x+3y+λz=μ has infinitely many solutions, then the value of λ+μ is:
- Let A = bmatrix 1&2&7 4&-2&8 3&8&-7 bmatrix and det(A−αI)=0, where α is a real number. If the largest possible value of α is p,...
- Let M be a 3×3 matrix such that M pmatrix 1 0 0 pmatrix = pmatrix 1 2 3 pmatrix , M pmatrix 0 1 0 pmatrix = pmatrix 0 1 2 pmatrix...
- Let A be a 3×3 matrix such that A^T bmatrix 1 0 1 bmatrix = bmatrix 5 2 2 bmatrix , A^T bmatrix 0 0 1 bmatrix = bmatrix 3 1 1...
- Let A= bmatrix -1&1&-1 1&0&1 0&0&1 bmatrix satisfy A²+α(adj(adj(A)))+β(adj(A))(adj(adj(A))) = bmatrix 2&-2&2 -2&0&-1 0&0&-1...
- If the system of linear equations: x + y + z = 6, x + 2y + 5z = 10, 2x + 3y + λz = μ has infinitely many solutions, then the...
- Let A= bmatrix &1&2 2&3&0 0&4&5 bmatrix and B= bmatrix 1&0&0 0&-5 &0 0&4 &-2 bmatrix + adj (A). If det(B) = 66, then det(adj(A))...
- Let B = bmatrix 1&3 1&5 bmatrix and A be a 2 × 2 matrix such that AB⁻¹ = A⁻¹. If BCB⁻¹ = A and C⁴ + αC² + βI = O, then 2β − α is...
- Let λ, μ ∈ ℝ. If the system of equations 3x + 5y + λz = 3, 7x + 11y − 9z = 2, 97x + 155y − 189z = μ has infinitely many...
- Let A be a non-singular matrix of order 3. If det(3adj(2adj((det A)A))) = 3⁻¹³·2⁻¹⁰ and det(3adj(2A)) = 2ᵐ·3ⁿ, then |3m + 2n| is...
- Let A be a 2 × 2 real matrix and I be the identity matrix of order 2. If the roots of the equation |A – xI| = 0 be –1 and 3, then...
- Consider the matrix f(x) = bmatrix x & - x & 0 x & x & 0 0 & 0 & 1 bmatrix Given below are two statements : Statement I : f(–x)...
- Let A = bmatrix 2 & 0 & 1 1 & 1 & 0 1 & 0 & 1 bmatrix , B = [B₁, B₂, B₃], where B₁, B₂, B₃ are column matrices and AB_1 = bmatrix...
Other chapters
Alcohols, Phenols and EthersAldehydes, Ketones and Carboxylic AcidsAlternating CurrentAminesAnatomy of Flowering PlantsAncient Indian HistoryAnimal KingdomApplication of DerivativesArea Under CurveAromatic Compounds and Aryl HalidesAtomsBasic Mathematics and LogarithmBinomial TheoremBiodiversity and ConservationBiological ClassificationBiomoleculesBiotechnology and Its ApplicationsBiotechnology: Principles and ProcessesBody Fluids and CirculationBreathing and Exchange of GasesCell Cycle and Cell DivisionCell: The Unit of LifeChemical Bonding and Molecular StructureChemical Coordination and Integration