GATE Questions & Answers of Eigen Values and Eigen vectors

What is the Weightage of Eigen Values and Eigen vectors in GATE Exam?

Total 9 Questions have been asked from Eigen Values and Eigen vectors topic of Linear Algebra subject in previous GATE papers. Average marks 1.67.

A system matrix is given as follows

A=01-1-6-116-6-115

The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is _______

Which one of the following statements is true for all real symmetric matrices?

A matrix has eigenvalues –1 and –2. The corresponding eigenvectors are 1-1 and 1-2 respectively. The matrix is

An eigenvector of p=110022003 is

The trace and determinant of a 2 × 2 matrix are known to be -2 and -35 respectively. Its eigen values are

The characteristic equation of a (3X3) matrix P is defined as

αλ=|λI-P|=λ3+λ2+1=0

If I denotes identity matrix, then the inverse of  matrix P will be

The linear operation L(x) is defined by the cross product L(x) = bXx, where b=[0 1 0]T and x=[x1 x2 x3]T are three dimensional vectors. The 3×3 matrix M of this operations satisfies Lx=Mx1x2x3

Then the eigenvalues of M are

Cayley-Hamilton Theorem states that a square matrix satisfies its own characteristic equation. Consider a matrix A=-32-10

A satisfies the relation

Cayley-Hamilton Theorem states that a square matrix satisfies its own characteristic equation. Consider a matrix A=-32-10

A9 equals