EGR599 (Fall 2002) ADVANCED ENGINEERING MATH ______

LAST NAME, FIRST (3 pts)

Quiz #1 (50 minutes)

Circle the correct answer or fill in the blanks.

You will earn 2 points for each correct answer to a maximum of 25 pts.

1.A = , the MATLAB statement A(1,:) = [1 2 3 4 5]

2.D = , D =

Xa.b. (1 + c)3 3(1 + c)c. (1 + c)3 + 2  3cd.None of the above

3.D =, D =

a. 1 + ax by  czb. 1 ax by + czX c. 1 ax by  czd.None of the above

4. Let A be partitioned so that A = , then An =

a.X b. c. d.None of the above

5.I. If A is nn and AB = 0 then B = 0

II. If A = where B and C are nonsingular, then A is nonsingular

a. I and II are trueb. Only I is trueX c. Only II is trued.I and II are false

6.I. If A and B commute, and if B-1 exists, then A and B-1 commute

II. If A is mn, B is nm, and AB = I then BA = AB

a. I and II are trueX b. Only I is truec. Only II is trued.I and II are false
7. Which of the following is true for all real matrices A and B.

a. (AT)-1 = (A-1)Tb. (AB)-1 = A-1B-1c. (AB)T = ATBT X d.None of the above

8. If A = then A-1 =

9.If A = , B = , and C = AB, then c22 = ____15______

10. I. If A2= 0 then A = 0

II. If (A +B)2 = A2+ 2AB + B2

a. I and II are trueb. Only I is truec. Only II is trueX d.I and II are false

11. The following MATLAB program can evaluate for x = 2

a.
x = 2;
sum = 1;
For n=0:10
sum = sum + (-1)^n*x^n/factorial(2*n+1);
end / c.
x = 2;
sum = 1; z = x;
For n=1:10
z = -z*x/(2*n+1); sum = sum+z
end
b.
x = 2;
sum = 1; z = 1;
For n=1:10
z = -z*x/(2*n+1); sum = sum+z
end / X d.
None of the above

12. If A is an nn invertible matrix then

I. The system Ax = b has a unique solution for every vector b.

II. The rows of A are linearly independent

a. I and II are trueb. Only I is trueX c. Only II is trued.I and II are false

13. If A is an nn invertible matrix then

I. A can be reduced (by elementary operations) to the identity matrix.

II. The rank A is n.

X a. I and II are trueb. Only I is truec. Only II is trued.I and II are false