Matrices questions
472 published questions with worked solutions.
- Let A = bmatrix 2&1&2 6&2&11 3&3&2 bmatrix and P = bmatrix 1&2&0 5&0&2 7&1&5 bmatrix . The sum of the prime factors of |P⁻¹AP −...
- Let A = bmatrix 1&0&0 0& & 0& & bmatrix and |2A|³ = 2²¹ where α, β ∈ ℤ, then a value of α is-
- Let A be a square matrix such that AAᵀ = I. Then 12A [(A + A^T)^2 + (A - A^T)^2 ] is equal to-
- Let R = pmatrix x&0&0 0&y&0 0&0&z pmatrix be a non-zero 3 × 3 matrix, where x sinθ = y sin(θ + 2π/3) = z sin(θ + 4π/3) ≠ 0, θ ∈...
- Consider the system of linear equations x + y + z = 5, x + 2y + λ²z = 9, x + 3y + λz = μ, where λ, μ ∈ ℝ. Then, which of the...
- Consider the system of linear equation x + y + z = 4μ, x + 2y + 2λz = 10μ, x + 3y + 4λ²z = μ² + 15, where λ, μ ∈ ℝ. Which one of...
- Let A be a 3 × 3 real matrix such that A pmatrix 1 0 1 pmatrix = 2 pmatrix 1 0 1 pmatrix , A pmatrix -1 0 1 pmatrix = 4 pmatrix...
- Let A be a 3 × 3 matrix and det(A) = 2. If n = det(adj(adj(…(adj A)))) (adj taken 2024 times), then the remainder when n is...
- If the system of linear equations x − 2y + z = −4, 2x + αy + 3z = 5, 3x − y + βz = 3 has infinitely many solutions, then 12α +...
- Consider the system of linear equations –x + y + 2z = 0, 3x – ay + 5z =1, 2x – 2y – az = 7. Let S_1 be the set of all a R for...
- Let J_ n,m = _0^1 x^n x^m-1 dx, n>m and n,m . Consider a matrix A=[a_ ij ]_ 3 3 where a_ ij = cases J_ 6+i,3 -J_ i+3,3 , & i j 0,...
- Let, A= bmatrix i&-i -i&i bmatrix , i= -1 . Then the system of linear equations A^8 bmatrix x bmatrix = bmatrix 8 64 bmatrix has -
- Let A= bmatrix a&b &d bmatrix and B= bmatrix bmatrix bmatrix 0 0 bmatrix such that AB = B and a + d = 2021, then value of ad – bc...
- Let I be an identity matrix of order 2 × 2 and P = bmatrix 2&-1 5&-3 bmatrix . Then the value of n N for which P^n=51-8P is equal...
- Let A+2B= bmatrix 1&2&0 6&-3&3 -5&3&1 bmatrix And 2A-B= bmatrix 2&-1&5 2&-1&6 0&1&2 bmatrix . If Tr(A) denotes the sum of all...
- Let A = a_ ij be a 3 × 3 matrix, where a_ ij = cases (-1)^ j-i , & i<j 2, & i=j (-1)^ i+j , & i>j cases then det(3Adj(2A^ -1 ))...
- Let A= bmatrix 2&3 &0 bmatrix , a R be written as P + Q where P is symmetric matrix and Q is skew symmetric matrix. If det(Q) =...
- Let A= pmatrix 1&-1&0 0&1&-1 0&0&1 pmatrix and B = 7A^ 20 -20A^7+2I, Where I is an identity matrix of order 3× 3. If B = [b_ ij...
- The values of and such that the system of equations x + y + z = 6, 3x + 5y + 5z = 26, x + 2y + = has no solution, are :
- Let A = [a_ ij ] be a real matrix of order 3 × 3, such that a_ i1 +a_ i2 +a_ i3 = 1, for i = 1, 2, 3. Then, the sum of all the...
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