Q: Given the matrix $$A = \begin{bmatrix} 1 & 2 \\ -4 & 6 \\ -3 & 5 \end{bmatrix}$$, what is $$3A$$?

$$\begin{bmatrix} 3 & 6 \\ -12 & 18 \\ -9 & 15 \end{bmatrix}$$

Q: Which of the following statements about matrix multiplication is TRUE?

Matrix multiplication is not commutative: $$AB \neq BA in $$general.

Question 1

Which of the following best describes an algorithm in the context of scientific computing?

Accepted Answer

A step-by-step description of a set of instructions to be executed in a certain order to get a desired output.

Question 2

Given the Python code below, what will be the output?

x = 5
y = 2
print(x // y)

Accepted Answer

$$2$$

Question 3

Which of the following is NOT a valid variable name in Python?

Accepted Answer

2myname

Question 4

Evaluate the following expression in Python: $$2/(2+1)*3$$

Accepted Answer

Question 5

Which of the following statements about Python data types is TRUE?

Accepted Answer

A string can be indexed and sliced like a list.

Question 6

What is the output of the following code?

info = ['Star Wars', 1977, 'PG', [35.9, 460.9]]
print(info[-1][-1])

Accepted Answer

$$460.9$$

Question 7

Which of the following best describes the difference between the 'if' and 'if-elif-else' statements in Python?

Accepted Answer

'if' can only check one condition, while 'if-elif-else' can check multiple conditions in sequence.

Question 8

Suppose you want to double every value in the list $$A = [7, 6, 8, 14, 25, 6]$$ using a for loop. Which of the following Python code snippets will achieve this?

Accepted Answer

B = [a*2 for a in A]

Question 9

Which of the following is the correct formula for the Newton-Raphson method for finding roots of $$f(x) = 0$$?

Accepted Answer

$$x_{i+1} = x_i - \frac{f(x_i)}{f'(x_i)}$$

Question 10

Given the matrix $$A = \begin{bmatrix} 1 & 2 \ -4 & 6 \ -3 & 5 \end{bmatrix}$$, what is $$3A$$?

Accepted Answer

$$\begin{bmatrix} 3 & 6 \ -12 & 18 \ -9 & 15 \end{bmatrix}$$

Question 11

Which of the following is the correct definition of the Euclidean norm ($$\$$ell_2$$ norm) of a vector v$$ = [$$v_1$$, $$v_2$$, ..., v_n]$$?

Accepted Answer

$$\|v\|_2 = \sqrt{\sum_{i=1}^n v_i^2$}$$

Question 12

Suppose you are using the bisection method to find a root of $$f(x) in$$ $$[a, b]. $$After $$n$$ iterations, what is the maximum possible error in your approximation?

Accepted Answer

$$\frac{b-a}{2^n}$$

Question 13

Which of the following statements about matrix multiplication is TRUE?

Accepted Answer

Matrix multiplication is not commutative: $$AB 
eq BA in $$general.

Question 14

If the relative error in an approximation is $$r$$, which of the following expresses the floating-point representation $$fl(x) in $$terms of the true value $$x$$?

Accepted Answer

$$fl(x) = x(1 \pm r)$$

Question 15

Which of the following Python statements will correctly import the numpy library for use in scientific computing?

Accepted Answer

import numpy as np

Question 16

Which of the following is a property of the identity matrix $$I_n$$?

Accepted Answer

$$AI_n = A$$ for any matrix $$A of $$appropriate size.

Question 17

Which of the following is a valid stopping criterion for the bisection method?

Accepted Answer

$$|b_n - a_n| \u003c \varepsilon$$

Question 18

Which of the following best describes the main advantage of using the nested form of a polynomial for evaluation?

Accepted Answer

It reduces the number of operations and minimizes round-off errors.

Scientific Computing I: Foundational Concepts for College Algebra Students

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