Download Sample test, num. math. practice

Sample test, num. math. practice
2017. március 24.
Each question has exactly one correct answer. Please circle exactly one answer indicating your choice.
Unanswered questions will be scored as incorrect. Correct answers worth 3 points, incorrect answers −1.
1. Floats
Let us consider the floating point number system
F = [a = 2, k− = −5, k+ = 5, t = 4].
1. What is largest number (M∞ ) in F ?
A. 32
B. 16
C. 30
D. 26
2. What is the smallest positive number (0 ) in F ?
A.
1
64
B.
1
30
C.
1
24
D.
1
32
3. What is the representation of
3
4
in F ?
A. −23 · 0.1100
B. +20 · 0.1100
C. +20 · 0.1000
D. +21 · 0.1101
4. How many positive numbers can be represented in F ?
A. 64
B. 32
1
C. 88
D. 11
2
Consider the vectors
a = (1, −1, 2) and b = (−3, 0, 4),
and the matrix

0
A= 2
−1
2. Norms
1. The 1-norm of a is:
A. −1
B. 2
C. 4
D. 1
2. The 2-norm of b is:
A. 5
B.
C.
1
2
√
5
D. 1
3. The ∞ norm of A is:
A. 0
B. 1
C. 8
D. 10
4. The 1 norm of A is:
A. 8
B. 10
C. 5
D. 12
3

1 −1
3 5
4 0
3. factorization
Consider the matrix

−2
1
−3
1
B = −1
2

3
−1
2
1. For the LU factorization of B:
A. l31 = −1, u22 = −2, l21 = 2
B. l11 = 1, u12 = 2, l21 = −1
C. l31 = 2, u22 = −1, l21 = −1
D. l31 = 1, u22 = −2, l21 = 2
***
Consider the matrix

1
C = −1
2
2. For the C = LLT (Cholesky) factorization
A. l31 = −1, l22 = 1 l21 = 2
B. l11 = 1, l12 = 2, l21 = −1
C. l21 = −1, l31 = 2, l32 = −1
D. l31 = 1, l22 = −2, l21 = 2
4
−1
2
−3

2
−3
6
4. least squares
Consider the point set P
(−1, 2), (−1, 1), (−1, −1), (2, 0), (2, 2).
1. The best approximating line for P is:
A.
13
54 t
B.
1
9t
C.
2
18 t
D.
7
9t
+
+
7
9
−
−
7
54
14
19
1
9
2. The best approximating quadratic polynomial is:
A. not uniquely determined by the points.
B. t2 − t + 2
C. t2 + t − 2
D. does not exist
***
Consider the pont set
1
1
1
Q = { ,8 ,
,6 ,
, 4 , (1, −2)}
4
3
2
1. The best fit function of the form a +
A.
5
16t
B.
8
5t
−
20
5
C.
16
5t
−
20
5
D.
6
17 t
b
t
for the set Q is:
−5
−
14
19
5