Matrices and Determinants
81 questions across 11 topics.
Matrices and Determinants
- 3Definiteness from trace and determinantIIT JAM 2026 MSMatrices and DeterminantsEasy
- 16Skew-symmetric orthogonal matricesIIT JAM 2026 MSMatrices and DeterminantsEasy
- 18Probability a random matrix is orthogonalIIT JAM 2026 MSMatrices and DeterminantsHard
- 32Rank facts for rectangular matricesIIT JAM 2026 MSMatrices and DeterminantsMedium
- 42Parameter sum for infinite solutionsIIT JAM 2026 MSMatrices and DeterminantsEasy
- 52Determinant via column operationsIIT JAM 2026 MSMatrices and DeterminantsHard
- 2Real characteristic roots of a circulantIIT JAM 2025 MSMatrices and DeterminantsMedium
- 13A rank statement that can failIIT JAM 2025 MSMatrices and DeterminantsHard
- 14Dimensions of successive imagesIIT JAM 2025 MSMatrices and DeterminantsHard
- 16Nonsingularity from an annihilating polynomialIIT JAM 2025 MSMatrices and DeterminantsMedium
- 32How many parameter pairs give infinite solutionsIIT JAM 2025 MSMatrices and DeterminantsHard
- 41L1 norm of characteristic coefficientsIIT JAM 2025 MSMatrices and DeterminantsEasy
- 3Sum of inverse and inverse adjointIIT JAM 2024 MSMatrices and DeterminantsMedium
- 16Rank and solvability of a 3 by 5 systemIIT JAM 2024 MSMatrices and DeterminantsHard
- 33Eigenvalues of A and of A plus A squaredIIT JAM 2024 MSMatrices and DeterminantsMedium
- 43Dimension of equal first two coordinatesIIT JAM 2024 MSMatrices and DeterminantsEasy
- 53Linear combination of orthogonal-matrix entriesIIT JAM 2024 MSMatrices and DeterminantsMedium
- 1Subspace containing eigenvector of matrix powerIIT JAM 2023 MSMatrices and DeterminantsMedium
- 2Row and column representations of productIIT JAM 2023 MSMatrices and DeterminantsEasy
- 27Parameter values for infinite solutionsIIT JAM 2023 MSMatrices and DeterminantsMedium
- 31Symmetric and skew-symmetric decomposition propertiesIIT JAM 2023 MSMatrices and DeterminantsMedium
- 35Adjoint matrix eigenvalues and traceIIT JAM 2023 MSMatrices and DeterminantsHard
- 3Maximum of a parameterized determinantIIT JAM 2022 MSMatrices and DeterminantsMedium
- 15Linear system with infinite solutionsIIT JAM 2022 MSMatrices and DeterminantsMedium
- 16Sum of elements of matrix powerIIT JAM 2022 MSMatrices and DeterminantsMedium
- 33Properties of orthogonal and skew-symmetric matricesIIT JAM 2022 MSMatrices and DeterminantsHard
- 43Trace of matrix from its adjointIIT JAM 2022 MSMatrices and DeterminantsMedium
- 53Unit eigenvector of symmetric matrixIIT JAM 2022 MSMatrices and DeterminantsHard
- 7Eigenvectors must stay independentIIT JAM 2021 MSMatrices and DeterminantsMedium
- 28Unique solution through the determinantIIT JAM 2021 MSMatrices and DeterminantsMedium
- 31An inconsistent system tells the rankIIT JAM 2021 MSMatrices and DeterminantsMedium
- 32When every row adds to oneIIT JAM 2021 MSMatrices and DeterminantsMedium
- 34Quadratic form on the unit circleIIT JAM 2021 MSMatrices and DeterminantsMedium
- 41Eigenvalues from trace and determinantIIT JAM 2021 MSMatrices and DeterminantsMedium
- 42Determinant of a quartic matrix polynomialIIT JAM 2021 MSMatrices and DeterminantsMedium
- 4Unique solution among parameter pairsIIT JAM 2020 MSMatrices and DeterminantsMedium
- 17Linear transformation on three anchor vectorsIIT JAM 2020 MSMatrices and DeterminantsEasy
- 18Cayley transform of a skew-symmetric matrixIIT JAM 2020 MSMatrices and DeterminantsMedium
- 34Orthogonal completion of a two-by-two matrixIIT JAM 2020 MSMatrices and DeterminantsMedium
- 44Rank of a four-by-four matrixIIT JAM 2020 MSMatrices and DeterminantsMedium
- 53Trace of a cube under similarityIIT JAM 2020 MSMatrices and DeterminantsMedium
- 54Matrix polynomials through eigenvaluesIIT JAM 2020 MSMatrices and DeterminantsMedium
Systems of linear equations
- 16Value of a combination fixed by two equationsIIT JAM 2018 MSSystems of linear equationsMedium
- 2Rank-one system with non-parallel vectorsIIT JAM 2017 MSSystems of linear equationsMedium
- 51Sum of absolute components of a unit null vectorIIT JAM 2017 MSSystems of linear equationsHard
- 31Solutions of a symmetric two by two linear systemIIT JAM 2016 MSSystems of linear equationsMedium
- 29Solution set of a consistent linear system with given rankIIT JAM 2015 MSSystems of linear equationsMedium
- 58Parameter value for which a linear system has no solutionIIT JAM 2015 MSSystems of linear equationsHard
- 22Parameter values for which a linear system has infinitely many solutionsIIT JAM 2014 MSSystems of linear equationsMedium
- 19Condition on parameters for a linear system to be always solvableIIT JAM 2013 MSSystems of linear equationsHard
Eigenvalues and eigenvectors
- 33Matrix whose every vector is an eigenvectorIIT JAM 2019 MSEigenvalues and eigenvectorsMedium
- 1Imaginary parts of eigenvalues of a block triangular matrixIIT JAM 2017 MSEigenvalues and eigenvectorsEasy
- 31Properties of a Householder reflectionIIT JAM 2017 MSEigenvalues and eigenvectorsHard
- 27Number of distinct eigenvalues of the all-ones matrixIIT JAM 2014 MSEigenvalues and eigenvectorsMedium
- 5Trace of the sum of the inverse and the square of a matrixIIT JAM 2013 MSEigenvalues and eigenvectorsMedium
- 1Eigenvector of a triangular matrix with a repeated eigenvalueIIT JAM 2012 MSEigenvalues and eigenvectorsEasy
Determinants
- 54Determinant of a four by four block matrixIIT JAM 2019 MSDeterminantsMedium
- 49Determinant of a product of column-replaced identitiesIIT JAM 2017 MSDeterminantsMedium
- 52Product of the eigenvalues of the inverse of a matrixIIT JAM 2016 MSDeterminantsMedium
- 25Consequence of a zero determinantIIT JAM 2015 MSDeterminantsEasy
- 27Number of values of the variable making a matrix singularIIT JAM 2015 MSDeterminantsMedium
Linear transformations
- 4Linear map given on a basis of R2IIT JAM 2019 MSLinear transformationsMedium
- 7Transformation that is not linearIIT JAM 2015 MSLinear transformationsEasy
- 6Which maps of three-space are linearIIT JAM 2014 MSLinear transformationsEasy
- 7Matrix of a linear transformation in a given basisIIT JAM 2014 MSLinear transformationsHard
Cayley-Hamilton theorem
- 18Inverse expressed through Cayley-HamiltonIIT JAM 2019 MSCayley-Hamilton theoremMedium
- 4Matrix equation from the characteristic polynomialIIT JAM 2018 MSCayley-Hamilton theoremMedium
- 30Matrix identity from known eigenvaluesIIT JAM 2016 MSCayley-Hamilton theoremHard
- 24Matrix equation satisfied by a two by two matrixIIT JAM 2015 MSCayley-Hamilton theoremMedium