Choose correct answer

1. If u and v are nonzero vectors in R3, then the properties listed below are true, except? *

a. u and v are parallel if and only if u x v = 0

b. The angle between u and v is found using x u = u v sin

c. The parallelogram between u and v as adjacent side has an area of u v.

d. u v is orthogonal to both u and v.

2. The cross product is defined only for vectors in . *

a. r3

b. R2

c. V3

d. R3

3. If u, v, and w are vectors in R3 and c is a scalar, then the properties listed below are true, except? *

a. u v = - (v u)

b. u (v w) = (u v)

c. u u = 0

d. u 0 = 0 u = 0

4. The length or norm of the vector is v = I v1 + v2 + v3 + . . . + vn I. *

a. True

b. False

5. The dot product of two vectors u and v is another vector represented by u v = (u1v1, u2v2, u3v3, ..., unvn). *

a. True

b. False

6. The angle between the zero vector and another vector is . *

a. angle

b. defined

c.

d. not defined

7. It can be characterized by two quantities the length and direction. *

a. Vectors

b. Length of a vector

c. Unit vectors

d. Vector length and unit vectors

8. He is credited as a significant contributor to the field of education for scientists, mathematicians and engineers. His work force mathematician to reconsider the accepted, but narrow, definition of a function. *

a. Gram-Schidt

b. Olga Taussky-Todd

c. Jean-Baptiste Joseph Fourier

d. John Kennedy

9. She was a distinguished and prolific mathematician, wrote many research papers in such areas as matrix theory, group theory, algebraic number theory and numerical analysis. *

a. Gram-Schidt

b. Olga Taussky-Todd

c. Jean-Baptiste Joseph Fourier

d. Vector

10. The four fundamental subspaces of the matrix A are listed below, except? *

a. N (A) = nullspace of A

b. N (AT) = nullspace of AT

c. R (A) = column space of A

d. A (RT) = column space of AT

11. The vector product is called the , and it is most conveniently defined and calculated when vectors written in standard unit vector form v = (v1,v2,v3) = v1i + v2j + v3k. *

a. product

b. vector product

c. inner product

d. cross product

12. An orthonormal basis derived by the Gram-Schmidt orthonormalization process does not depend on the order of the vectors in the basis. *

a. True

b. False

13. A set S of vectors in an inner product space V is orthogonal when every pair of vectors in S is orthogonal. *

a. True

b. False

14. It comes from the fact that minimizing Ax-b is equivalent to the minimizing Ax-b2, which is a sum of squares. *

a. orthogonal subspace

b. least squares

c. orthogonal complement

d. orthogonal projection and distance

15. The least squares problem is to find x in Rn such that Ax-b2 is minimized. *

a. True

b. False