Mathematical Methods

True or False Statements

Chapter 1 Matrices and Linear Systems of Equations

1. In a diagonal matrix some of the diagonal elements may be zero

Ans: T

2. The product of two nonzero matrices is always a nonzero matrix

Ans: F

3. The rank of a singular matrix is one less than its order

Ans: F

4. The sum of two nonsingular matrices is always nonsingular

Ans: F

5. The product of two matrices is singular if either of them is singular

Ans: T

6. The system x − y = 2, x + y = 0 has a unique solution

Ans: T

7. The system x + y = 2, 2x + 2y = 4 has an infinite set of solutions

Ans: T

8. The system x + 2y = 1, 3x + 2y = 4 has no solution

Ans: F

Chapter 2 Eigenvalues and Eigenvectors

9. A matrix and its inverse have the same eigenvalues if A is orthogonal ...