# 2/ Exercise solutions


```python
# setup SymPy
from sympy import *
x, y, z, t = symbols('x y z t')
init_printing()
```


```python

```

## Definitions


```python

```


```python

```

### E2.1


```python

```


```python

```

### E2.2

Given the matrices $A=\begin{pmatrix}1 & 3 \\ 4 & 5\end{pmatrix}$ and $B=\begin{pmatrix} -1 & 0 \\ 3 & 3 \end{pmatrix}$, 
and the vectors $\vec{v}=\begin{pmatrix}1 \\  2\end{pmatrix}$ and $\vec{w}=\begin{pmatrix}-3 \\ -4\end{pmatrix}$,
compute the following expressions.

- a) $A\vec{v}$
- b) $B\vec{v}$
- c) $A(B\vec{v})$
- d) $B(A\vec{v})$
- e) $A\vec{w}$
- f) $B\vec{w}$



```python
# define the matrices A and B, and the vecs v and w
A = Matrix([[1,3],
            [4,5]])
B = Matrix([[-1,0],
            [ 3,3]])
v = Matrix([[1,2]]).T     # the .T makes v a column vector
w = Matrix([[-3,-4]]).T
```


```python
# a)
A*v
```


```python
# b)
B*v
```


```python
# c)
A*B*v
```


```python
# d)
B*A*v
```


```python
# e)
A*w
```


```python
# f)
B*w
```

### E2.3


```python

```


```python

```

## Vector operations


```python

```


```python

```

### E2.4


```python

```


```python

```

### E2.5


```python

```


```python

```

### E2.6 


```python

```


```python

```

## Matrix operations


```python

```


```python

```

### E2.7


```python

```


```python

```

### E2.8


```python

```


```python

```

### E2.9


```python

```


```python

```

## Linearity


```python

```


```python

```

### E2.10


```python

```


```python

```

cd2639fb9defefabe375dd473fe6cf08f0aec3d1
ipynb
Jupyter Notebook
chapter02_exercises.ipynb
minireference/noBSLAnotebooks
3d6acb134266a5e304cb2d51c5ac4dc3eb3949b4
MIT
2016-04-20T13:56:02.000Z
2022-03-30T08:55:08.000Z
chapter02_exercises.ipynb
minireference/noBSLAnotebooks
3d6acb134266a5e304cb2d51c5ac4dc3eb3949b4
MIT
2021-07-01T17:00:38.000Z
2021-07-01T19:34:09.000Z
chapter02_exercises.ipynb
minireference/noBSLAnotebooks
3d6acb134266a5e304cb2d51c5ac4dc3eb3949b4
MIT
2017-02-04T05:22:23.000Z
2021-12-28T00:06:50.000Z
Qwen/Qwen-72B
1. YES
2. YES