In the following, let A = [1 5 4; 2 7 8; 3 2 5] and B = [1 0 0; 0 4 2; 0 2 9] be matrices, C = [1 3 3] be a vector and D = [4 7 9 3 12 11 2 8 8] be data.

1. Compute the mean of data D.

2. Compute the inverse of A and of B.

3. Compute the transpose of [A + B].

4. Add the (2,3) component of A to the (3,1) component of B.

5. Compute the matrix product A * B.

6. Compute the determinant of A.

7. Write a function for a two-dimensional Gaussian of mean mu and covariance Sigma. Let mu = (-2,7) and Sigma = [1 0; 0 2]. Compute the value of your Gaussian at the point (-3,1).

8. Plot your Gaussian in two dimensions in the range (-10 < x < +10), (-10 < y < 10).

9. Plot 3.5 sin(1.6 x) for (-5 < x < +5).