MTH501 Quiz 4

Q1. The matrix A^T(Transpose of A) x A is ________ if and only if the columns of A are linearly independent.

1. symmetric
2. invertible
3. scalar
4. singular

Correct answer: invertible

Q2. Two vectors u and v are orthogonal to each other if _____________.

1. u + v = 0
2. u . v = 0
3. u . v = 1
4. u - v = 0

Correct answer: u . v = 0

Q3. Each pair of eigenvalue and its corresponding eigenvectors provides a solution of the equation x' = Ax which is called

1. eigenfunctions
2. dynamical system
3. solution matrix
4. vector space

Correct answer: eigenfunctions

Q4. If a _____ matrix has orthonormal columns, then it also has orthonormal rows.

1. rectangular
2. diagonal
3. square
4. singular

Correct answer: square

Q5. Two vectors u and v in R^n are orthogonal if ------

1. u.v=0
2. u.v 0

Correct answer: u.v=0

Q6. A square matrix with orthogonal columns is ________ matrix.

1. an nonivertible
2. an invertible
3. an orthonormal
4. an orthogonal

Correct answer: an orthogonal

Q7. Let s = \{ {u_1} + {u_2} + ......{u_p}\} be a basis for a subspace W of {R^n} , is also an orthogonal basis if S is an orthogonal set.

1. False
2. True

Correct answer: True

Q8. For a real matrix A, complex Eigen values and associated Eigen vectors come in ---------

1. conjugate pairs
2. similar pairs
3. Complex pairs
4. none of the above

Correct answer: conjugate pairs

Q9. If the columns of a matrix are ________ then the matrix is invertible.

1. linearly dependent
2. linearly independent

Correct answer: linearly independent

Q10. Any orthogonal subsets of vector in an inner product space is linearly independent

1. True
2. False

Correct answer: True