MTH501 Final Term Solved MCQs Set 4

Q1. Which statement about the General Least Square Method is true?

•  Solution obtained by this method is always Unique.
•  This is a numerical method for the solution of system of Linear Equations.
•  This method find an X that make Ax as close possible to the b.
•  This method gives us exact solution of the System.

2. Let v = (1, -2, 2, 0). The unit vector in the same

, , , 0

•  1 2 2 , 0 1 2 2 1

3. Let u = (3, -2), v= (4, 5). For the weighted Euclidean inner product (u, v) = 4u1v1 + 5 u2v2 (v, u) = 2

•  -2

3

•  -3
•  Attractor

8. Suppose that A =

0.5

0.6 has eigenvalues 0.8 and

-0.3 1.4 

1.1. then 0rigin is a

•  Repellor
•  Attractor

9. if A is an m x n matrix with linearly independent column vector, then A can be factored as

A= QR

Where Q is an m X n matrix orthonormal column vector ,and R is an n x m.

•  Upper triangular matrix
•  Invertible matrix
•  Invertible lower triangular matrix
•  invertible Upper triangular matrix

10. The matrix equation AT A x^ = AT b represent a system of liner equation Commonly referred to as the

•  Normal equation for x
•  Normal equation for X^
•  Normal equation for A
•  Normal equation for b

11. By the best Approximation theorem , the distance from y to W is ||y – Y^|| , where Y^=

•  Projw Y^
•  Projwy  is
•  projy W

12. ||u + v + w|| ||u|| + ||v|| +||w|| for all vectors u, v and w in an inner product space.

•  True
•  False

13. The dominate for the matrix A =

•   =1 0 0 0  1 0 0 -3 0  0
•   = -1
•   = 0

14. A square matrix A I invertible if and only if and only is X = 0 is not an Eigen Value of A

•  True
•  False

15. A square matrix with orthogonal columns ----------- -------matrix.

•  Is an orthogonal
•  May be an orthogonal
•  May not be an orthogonal
•  Is not an orthogonal

16. if two row are orthogonal , they are -------------- --.

•  Linearly independent
•  Linearly Dependent
•   = -3