Determinants questions
307 published questions with worked solutions.
- Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + bz, y = az + cx and...
- Let a, b, c be such that b(a + c) 0. If vmatrix a & a + 1 & a - 1 -b & b + 1 & b - 1 & c - 1 & c + 1 vmatrix + vmatrix a + 1 & b...
- The number of values of k for which the linear equations 4x + ky + 2z = 0; kx + 4y + z = 0; 2x + 2y + z = 0 possess a non-zero...
- For the system x - y + z = 4, 2x + y - 3z = 0, x + y + z = 2, the values of x, y, z respectively are given by
- If A= bmatrix 1&1&1 2&1&-3 -1&2&3 bmatrix , then A_ 31 +A_ 32 +A_ 33 = where A_ ij is cofactor of a_ ij , where A=[a_ ij ]_ 3 3
- If A = bmatrix 0 & 1+2i & i-2 -1-2i & 0 & K 2-i & 7 & 0 bmatrix and A^ -1 does not exists, then K = (where i = -1 )
- If A=[a_ ij ]_ 3 3 = bmatrix 1&2&3 1&1&5 2&4&7 bmatrix and A_ ij is a cofactor of a_ ij , then a_ 11 A_ 21 +a_ 12 A_ 22 +a_ 13 A_...
- If vmatrix (A+B) & - (A+B) & 2B A & A & B - A & A & B vmatrix = 0, then the value of B is
- If A = [a_ ij ]_ 3 3 = bmatrix 1 & 3 & 3 -1 & 2 & 2 1 & 1 & 4 bmatrix and A_ ij is a cofactor of a_ ij then the value of a_ 31 A_...
- If A=[a_ ij ]_ 3 3 = bmatrix 3&2&4 1&4&1 2&6&3 bmatrix and A_ ij is a cofactor of a_ ij , then the value of a_ 21 A_ 21 +a_ 22 A_...
- If A= bmatrix 1&2&3 -1&1&2 1&2&4 bmatrix and A_ ij is a cofactor of a_ ij , then the value of a_ 21 A_ 21 +a_ 22 A_ 22 +a_ 23 A_...
- If A= bmatrix & &0 - & &0 0&0&1 bmatrix , where A_ 21 ,A_ 22 ,A_ 23 are cofactors of a_ 21 ,a_ 22 ,a_ 23 respectively, then the...
- Let A = bmatrix 3 & 1 & 2 1 & 2 & 0 1 & 1 & 4 bmatrix and pC_ 11 + 4C_ 21 - 5C_ 32 = -2, where C_ ij denotes the cofactor of an...
- If vmatrix -2a & a + b & a + c + a & -2b & b + c + a & b + c & -2c vmatrix = (a + b)(b + c)(c + a) 0 then α is equal to
- If a, b, c, are non zero complex numbers satisfying a^2 + b^2 + c^2 = 0 and vmatrix b^2 + c^2 & ab & ac & c^2 + a^2 & bc & bc &...
- Statement 1: If the system of equations x + ky + 3z = 0, 3x + ky − 2z = 0, 2x + 3y − 4z = 0 has a nontrivial solution, then the...
- Let P and Q be 3 × 3 matrices with P ≠ Q. If P^3 = Q^3 and P^2Q = Q^2P, then determinant of (P^2 + Q^2) is equal to
- If a, b, c are sides of a scalene triangle, then the value of vmatrix a & b & c & c & a & a & b vmatrix is :
- Statement-1: The system of linear equations x + ( )y + ( )z = 0 x + ( )y + ( )z = 0 x - ( )y - ( )z = 0 has a non-trivial...
- Let S = pmatrix a_ 11 & a_ 12 _ 21 & a_ 22 pmatrix : a_ ij 0, 1, 2 , a_ 11 = a_ 22 Then the number of non-singular matrices in...
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