Use Python:

Define the following vectors and matrices:

vec1 = np.array([ -1., 4., -9.])

mat1 = np.array([[ 1., 3., 5.], [7., -9., 2.], [4., 6., 8. ]]

1. You can multiply vectors by constants. Compute

vec2 = (np.pi/4) * vec1

2. The cosine function can be applied to a vector to yield a vector of cosines.

Compute

 vec2 = np.cos( vec2 )

3. You can add vectors and multiply by scalars. Compute

vec3 = vec1 + 2 * vec2

4. The Euclidean norm of a matrix or a vector is available using la.norm.

Compute

la.norm(vec3)