# PHYCS 3730/6720 Lab Exercise

This exercise provides practice with the numpy linear algebra package.

The answer file is Mylab10.txt.

#### Exercise 1. Solving a linear system

Solve the linear system Ax = b using Python numpy in interactive mode. Paste your Python session with its solution into your answer file.
``` Eqn (1)   2*x1 -   x2 +   x3 =  -1
Eqn (2)   3*x1 + 3*x2 + 9*x3 =   0
Eqn (3)   3*x1 + 3*x2 + 5*x3 =   4
```

#### Exercise 2. Check your solution with Python

Continue your interactive Python session from Exercise 1. Check your answer by multiplying the matrix A by your solution vector x, subtract the vector b. Print the difference vector. Then take the Euclidean norm (length) of the difference vector. That is, calculate d = Ax-b and |d| = |Ax - b|. Copy the new lines in your interactive session to your answer file. Hint. Don't use * when multiplying matrix with a vector. Use the np.dot function instead. See the notes linked above.

#### Exercise 3. Matrix inverse

Continue your interactive Python session from Exercise 2. Compute and print the inverse of the matrix A (call it Ainv). Then with Python show that
• Ainv*A = I
• A*Ainv = I
• Ainv*b = x
Copy the new lines in your interactive session to your answer file.