Eigenvalues and Matrices Quiz

Eigenvalue of a square matrix A are roots of differential equation

• characteristic equation

• integral equation

• logical equation

A matrix which is formed by turning all rows of a given matrix into columns and vice-versa is called

• skew matrix

• transpose matrix

• augmented matrix

• identity matrix

If 1 and 2 are eigen values of a 2×2 matrix A, what are the eigen values of A2 and A-1.

• Eigen values of A2 = 1, 4 and Eigen values of A-1 = 1,12

• Eigen values of A2 = 1, 2 and Eigen values of A-1 = 1,12

• Eigen values of A2 = 1, 4 and Eigen values of A-1 =12,14

• None of the above

The sum of the eigenvalues is equal to

• the product of diagonal elements

• DetA

• sum of the diagonal elements

• product of eigenvalues

According to Cayley- Hamilton Theorem, state which of the following is TRUE.

• Every skew matrix satisfies its own characteristic equation

• Every matrix satisfies its own characteristic equation

• Every square matrix satisfies its own characteristic equation

• Every square matrix does not satisfy its own characteristic equation

The rank of the quadratic form is

• No. of positive eigenvalues

• No. of positive eigenvalues - No. of negative eigenvalues

• No. of non-zero eigenvalues

• None of the above

The eigenvalues of A and B are same. What can you say about matrix B?

• B is equal matrix

• B is transpose of A

• both a) and b)

• none of the above

The eigenvalue of a real symmetric matrix is

• Real

• Imaginary

• Zero

• None

The eigenvector corresponding to distinct eigenvalues of a real symmetric matrix are

• Orthogonal

• unitary

• have repeated vectors

• does not exist

If A is a singular matrix of order 3 and 2, 3 are two eigenvalues find the 3rd eigenvalue.

• 2

• 3

• 0

• 6