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Syllabus of Linear Algebra- Vector space, Linear dependence of vectors, Basis, Dimension, Linear transformations, Matrix representation with respect to an ordered basis, Range space and null space, Rank-nullity theorem, Rank and inverse of a matrix, Determinant, Solutions of system of linear equations, Consistency conditions, Eigenvalues and eigenvectors, Cayley-Hamilton theorem, Symmetric, Skew-symmetric, Hermitian, Skew-Hermitian, Orthogonal and unitary matrices.
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symmetric matrix eigenvalues and Eigenvectors Diagonalization Gate 2003 linear algebra mathematics
Since M is symmetric so b not true. Now take a=b=c then matrix has 2 eg values 0 &other is trace . Hence opt a &c not possible.
Gate MA 2003, 35
Key (d)
