Crowdly

Add to Chrome

Mathematics for Computer Scientists 2 (COMP1045 UNMC) (SPM1 25-26)

Looking for Mathematics for Computer Scientists 2 (COMP1045 UNMC) (SPM1 25-26) test answers and solutions? Browse our comprehensive collection of verified answers for Mathematics for Computer Scientists 2 (COMP1045 UNMC) (SPM1 25-26) at moodle.nottingham.ac.uk.

Get instant access to accurate answers and detailed explanations for your course questions. Our community-driven platform helps students succeed!

Given the linear system A, what is the correct u33 in LU factorization?

Click here to find the formula which would be helpful to calculate u33

A =

2	1	1
4	1	0
-2	2	5

, L =

1	0	0
2	1	0
-1	-3	1

, and U =

2	1	1
0	-1	-2
0	0	u33

$\text{If } A = \begin{bmatrix} 2 & -1 \\ 0 & 3 \end{bmatrix}, \text{ then } 3A = ?$ \text{If } A = \begin{bmatrix} 2 & -1 \\ 0 & 3 \end{bmatrix}, \text{ then } 3A = ?

$\begin{bmatrix} 6 & -3 \\ 0 & 12 \end{bmatrix}$ \begin{bmatrix} 6 & -3 \\ 0 & 12 \end{bmatrix}

$\begin{bmatrix} 6 & -3 \\ 0 & 3 \end{bmatrix}$ \begin{bmatrix} 6 & -3 \\ 0 & 3 \end{bmatrix}

$\begin{bmatrix} 6 & -3 \\ 0 & 1 \end{bmatrix}$ \begin{bmatrix} 6 & -3 \\ 0 & 1 \end{bmatrix}

$\begin{bmatrix} 6 & -3 \\ 0 & 9 \end{bmatrix}$ \begin{bmatrix} 6 & -3 \\ 0 & 9 \end{bmatrix}

50%

View this question

What is the determinant of the matrix A and B?

$A = \begin{bmatrix} 1 & 0 & 0 &0\\ 0 & 2 & 0&0 \\ 0 & 0 & 3 & -1 \\ 0 & 0 &0&4\end{bmatrix}$ A = \begin{bmatrix} 1 & 0 & 0 &0\\ 0 & 2 & 0&0 \\ 0 & 0 & 3 & -1 \\ 0 & 0 &0&4\end{bmatrix}

$B = \begin{bmatrix} 3 & 0 & 0 &0\\ 0 & 3 & 0&0 \\ 0 & 0 & 3 & -2\\ 0 & 0 &0&1\end{bmatrix}$ B = \begin{bmatrix} 3 & 0 & 0 &0\\ 0 & 3 & 0&0 \\ 0 & 0 & 3 & -2\\ 0 & 0 &0&1\end{bmatrix}

$\det(A) =-24 \quad \text{and} \quad \det(B) =-27$ \det(A) =-24 \quad \text{and} \quad \det(B) =-27

$\det(A) = 24 \quad \text{and} \quad \det(B) = 27$ \det(A) = 24 \quad \text{and} \quad \det(B) = 27

$\det(A) = -6 \quad \text{and} \quad \det(B) = -9$ \det(A) = -6 \quad \text{and} \quad \det(B) = -9

$det (A) = 6 \quad \text{and} \quad det (B) = 9$ det (A) = 6 \quad \text{and} \quad det (B) = 9

17%

View this question

Consider the function f: A -> B, where A = {1, 2, 3} and B = {a, b, c}. The function is defined by the following mapping: 1 -> a, 2 -> b, 3 -> c. Which of the following describes the function?

Injective, Surjective, and Bijective

View this question

$\text{if} \quad A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \quad \text{, what is AB} \quad$ \text{if} \quad A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \quad \text{, what is AB} \quad

Python

import numpy as np
A = np.array([[1, 0, 0, 0], [0, 2, 0, 0], [0, 0, 3, -1], [0, 0, 0, 4]])
B = np.array([[3, 0, 0, 0], [0, 3, 0, 0], [0, 0, 3, -2], [0, 0, 0, 1]])
det_A = np.linalg.det(A)
det_B = np.linalg.det(B)
print(f"{det_A=}")
print(f"{det_B=}")

Code output

det_A=23.999999999999993
det_B=27.0

$\begin{bmatrix} 2 & 1 \\ 4 & 3 \end{bmatrix}$ \begin{bmatrix} 2 & 1 \\ 4 & 3 \end{bmatrix}

$\begin{bmatrix} 1 & 2 \\ 4 & 3 \end{bmatrix}$ \begin{bmatrix} 1 & 2 \\ 4 & 3 \end{bmatrix}

25%

$\begin{bmatrix} 2 & 1 \\ 1 & 4 \end{bmatrix}$ \begin{bmatrix} 2 & 1 \\ 1 & 4 \end{bmatrix}

25%

$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}

View this question

Given the linear system A, what is the correct u33 in LU factorization?

Click here to find the formula which would be helpful to calculate u33

A =

2	1	1
4	1	0
-2	2	3

, L =

1	0	0
2	1	0
-1	-3	1

, and U =

2	1	1
0	-1	-2
0	0	u33

What is the result of adding the following matrices ?

$\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}

and

$\begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix}$ \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix}

$\begin{bmatrix} 5 & 12 \\ 21 & 32 \end{bmatrix}$ \begin{bmatrix} 5 & 12 \\ 21 & 32 \end{bmatrix}

$\begin{bmatrix} 4 & 4 \\ 4 & 4 \end{bmatrix}$ \begin{bmatrix} 4 & 4 \\ 4 & 4 \end{bmatrix}

$\begin{bmatrix} 6 & 8 \\ 10 & 12 \end{bmatrix}$ \begin{bmatrix} 6 & 8 \\ 10 & 12 \end{bmatrix}

33%

$\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}

View this question

Gaussian elimination transforms a matrix into:

Transpose form

Reduced row echelon form

LU factorization decomposes a matrix into:

Symmetric and skew-symmetric matrices

60%

Diagonal and orthogonal matrices

20%

Identity and zero matrices

Lower and upper triangular matrices

20%

View this question

LU factorization is computationally efficient for:

Calculating determinants

Solving multiple systems with the same coefficient matrix

67%

Finding eigenvalues

33%

Solving a single system

View this question

Want instant access to all verified answers on moodle.nottingham.ac.uk?

Get Unlimited Answers To Exam Questions - Install Crowdly Extension Now!

Add to Chrome

Telegram Instagram TikTok Question Bank