Assignment 4: Vectors and Matrices
DTSC 680: Applied Machine Learning
Directions:
The purpose of this assignment is for you to become more familiar with the mathematical entities you have been indirectly dealing with all semester: vectors and matrices. This assignment has you perform basic vector and matrix arithmetic: adding and subtracting of vectors and matrices, multiplying vectors by matrices, and also matrix multiplication.
The following videos contain the information needed to understand these concepts, and answer the simple questions asked here.
What are Vectors?
Adding and Subtracting Vectors
What is a Matrix?
Adding and Subtracting Matrices
Multiplying Vectors and Matrices
Matrix Multiplication
Submission Directions:
You have one opportunity to submit your work. Submissions are collected through Brightspace. Your submission document must be a PDF. Your final submission PDF must include a “cover page” that contains your name, the class name and number, the assignment number, and (most importantly) your final answers that are neatly written for the following 14 problems. Be sure to clearly number your answers. This cover page may be typed or handwritten. The remainder of your final submission PDF must be pictures of your handwritten work. You must include pictures of your work that clearly show your calculations - do not use software to compute the answers for you (although feel free to check if your solutions are co
ect!) You must show your work for every problem below, and it must be legible. Be sure that your pictures are (reasonably) cropped, in-focus, and generally acceptable. Be sure your pictures are large enough to read - one picture per page is a good rule of thumb. Please box-in your final answers on the pages showing your calculations.
How to Submit a PDF through Brightspace
Your final PDF submission must be uploaded to Brightspace. The red oval in the following screenshot shows the “Add a File” button on the Assignment_4 submission page. Click this button to upload your submission PDF, then click “Submit” when you are done.
Problems:
Vector Arithmetic: Perform the following calculations for u and v.
1. u - v
2. u + v
3. 3u - 5v
4. 2u + 4v
Matrix Arithmetic: Perform the following calculations for A and B.
5. A + B
6. A - B
7. 2A - 3B
8. 5A + 2B
Matrix/Vector Multiplication: A matrix, A, can be viewed as a linear transformation, and matrix-vector multiplication can be understood as performing a linear transformation on a vector, x, to yield a new, transformed vector called b. Perform the following calculations of the form Ax = b to solve for b using the following values of A, B, u, v, and w. (In short, perform the following matrix-vector multiplications.)
9. Au
10. Bv
11. Aw
Matrix Multiplication: Perform the following matrix multiplication operations for A, B, C, and D that are given below.
12. AB
13. BA
14. CD