PART I $($Both Manual and Using Java$($or any other programming language of your choice$)$

For the following three problems, you will first compute solutions by hand $($show as many

steps as possible, including transpositions$).$ Then, use programming to compute the same

solution. Submit your codes a single PDF document along with your handwritten work

$($write comments to describe what your code is doing$).$ Feel free to also use popular

computational packages.

Question $1$: $(20$ points$)$

Compute the norm of $($:$3,1,2$:$).$

Question $2$: $(20$ points$)$

Compute the product $A^{T}x$ given that:

$A=\left[\begin{array}{ccc}4& -2& 1\\ 5& 7& -1\end{array}\right],x=\left[\begin{array}{c}2\\ 3\end{array}\right]$

Question $3$: $(25$ points$)$

Compute the determinant

$|[3,4,3],[-1,9,-1],[7,2,7]|$

Question $4$: $(5$ bonus points$)$

Compute the determinant

$|[8,-1],[0,2]|$

PART II

The next questions are programming related. Java is the recommended language. Please make sure

to include your code as a part of the pdf file.

Question $1$:$(15$ points$)$

Write down a matrix multiplication code for multiplying two arbitrary matrices. $(15$ points$)$: This function

should use popular packages $($i$.$e$.$ if you are using python, use the numpy package$)$ to achieve the same

result.

Question $2$:$(20$ points$)$

Solve the following system of equations

$2x_1+2x_2+6x_3=24$

$2x_1-2x_2-2x_3=0$

$4x_1+2x_2-4x_3=6$