Questions -

Q1. What is 5-norm of [[4,5,6],[6,7,8],[7,8,9]]?

23

26.39

25

Q2. What is the second derivative for sin(x)cos(x)?

-cos(2x)

-2sin(2x)

-sin(x)cos(x)

-2sin(x)cos(x)

Q3. Which on is wrong in python?

x = [1:2]

x = [1,2]

x = {1, 2}

x = (1, 2)

Q4. What is the oct value for 1111?

2127

2129

2128

2125

2124

Q5. What does integral measure?

above the curve

under the curve

on the curve

Q6. In python, which one is incorrect?

9 / 2 == 9//2

int(9.2) = 9

Q7. In python, what is the type of number 5.60?

bool

float

int

Q8. What does an integral measure?

area between the curve and y=x

area above the curve

area under the curve

some function of the curve

Q9. In Python, the def statement defines a function or method.

False

True

Q10. What is the uncertainty of the output if z =f(x)?

z= f'(x)

∂x = ∂z

∂z = f'(x)∂x

Q11. True or False: Total error = computational error + propagated data error

True

False

Q12. True of False: A problem is well posted if the solution has a continuous dependence on input data (a small change in the input causes a small change in the output)

False

True

Q13. Is it true or false that a lower triangular matrix has zeros above the diagonal elements?

True

False

Q14. When does Cholesky algorithm fail?

When the input matrix is not a positive definite.

All of the above

When the input matrix is not symmetric.

Q15. In python, what is the type of number 3?

int

float

bool

Q16. True or False: Linear algebra is the extension of elementary algebra to matrices (and vectors, which can be seen as special types of matrices)by defining the four elementary operations among them.

False

True

Q17. What is computational error?

the difference between f(x) and x

the difference between x and avg x

the difference between avg f(x) and y

the difference between avg f(x) and x

Q18. If the determinant of a matrix is zero, then it's inverse matrix is also zero.

False

True

Q19. Which expression has different value of others in python?

1 / 2 + 1 / 2

3 // 2

2 - 1

0 - -1

Q20. Which of the following expression have syntax error in python?

i++

i = i + 1

i += 1

i = 1 + 1

Q21. How do you import the entire content of a library?

import *

import +

import -

import data

Q22. Which one is False if i == 1?

before ++i, i is 2

after ++i, i is 2

Q23. Ture or False: Support vector machines try to maximize margin by solving a quadratic optimization problem.

True

False

Q24. Given a function f, we can approximate its integral by dividing its domain into n rectangles with width 1/n and height f(n). We can get better approximations for this integral by...

Increasing n.

Decreasing n.

Using trapezoids instead of rectangles and increasing n.

You cannot approximate an integral using this method.

Using trapezoids.

Q25. In Python, we can obtain a list of object attributes (including methods) for any object using the command dir.

True

False

Q26. True or False: If an inverse, A-1 exists, it is unique.

False

True

It depends on the matrix

Q27. Python supports multiple programming paradigms, including object oriented (class), imperative (def), and functional (lambda) programming.

False

True

Q28. What is the reason for systematic error?

A modeling errors (we do not know f (x))

A and B

Rounding errors (we do not implement f (x) with arbitrary precision arithmetic's).

Q29. When we take a set of observations of vectors that are possibly correlated and convert it to a set of vectors that are not correlated, the mathematical procedure is called:

Principal Component Analysis.

Curve-fitting.

Quadrature.

Golden section search.

Linear Least Squares.

Q30. Let f(x)f(x) = cos2(x)-sin2(x)cos2(x)-sin2(x). Compute ∫_π/40f(x)dx∫0π/4f(x)dx.

-1/2

ππ

1/2

π/2π/2

0

Q31. A Fourier transformation uses a vector to approximate a function with a domain over a finate interval.

False

True

Q32. Which is an example of a statistical distribution of data?

Gaussian

Exponential

Binomial

Poisson

All of these.

Q33. Which is a type of algorithm used to cluster data?

Centroid-based clustering

All of these.

Distribution-based clustering

Hierarchial clustering

Q34. When converting very large, sparse matrices, the best algorithm we discussed was ___, because___.

Minimum residual algorithm; if a solution exists, the minimum residual diverges.

Minimum residual algorithm; if a solution exists, the minimum residual converges to it.

Stabilized bi-conjugate gradient method; it is slower than minimum residual with a smoother convergence.

Stabilized bi-conjugate gradient method; it is faster than minimum residual with a smoother convergence.

Gauss-Jordan elimination; this is the only practical algorithm to use.

Q35. In a geometric representation, the scalar product relates to the angle (αα) between 2 vectors:

a'b = ||a|| *||b||*tan(αα)

a'b = ||a|| *||b|| *cos(αα)

a'b = (||a|| +||b||) *(||a|| -||b||)* cos(αα)

a'b = ||a|| *||b||*sin(αα)

Q36. We can use the _____ algorithm on a _____ matrix to determine if the matrix is ________.

Linear least squares; singular; positive-definite.

Jacobi; symmetric; sparse.

Cholesky; symmetric; positive-definite.

Minimum residual; non-symmetric; sparse.

Q37. Given variable x and integers n and C, the general integral of the power function x^n is...

x^(n+C)

(x^n-1)/n+1 +C

(nx)^n-1 +C

(x^n+1)/n+1 +C

Q38. The list.append(x) is one of the method of list objects. It adds an item to the end of the list. Equivalent to:

a[len(a):] = [x]

a[:len(a)] = [x]

a[-1:] = [x]

a[len(a)] = [x]

Q39. What is the inverse of [[2,3],[7,4]]

[[-4/13, 3/13], [7/13, -2/13]]

[[7/13, 3/13], [-4/13, -2/13]]

[[-2/13, 3/13], [7/13, -4/13]]

Q40. Solve this system of linear equations:

3x+2y-z=12x-2y+4z=-2-x+1/2y-z=03x+2y-z=12x-2y+4z=-2-x+1/2y-z=0

x=-1y=-2z=-2x=-1y=-2z=-2

x=1y=-2z=-2x=1y=-2z=-2

x=-2y=22z=-2x=-2y=22z=-2

x=1y=2z=2