Find the area of a parallelogram if it is defined by v = [2, 3] and w = [4, 1].

The area of a parallelogram defined by two vectors can be found using the cross product of the vectors. The magnitude of the cross product of two vectors gives the area of the parallelogram that they span.

The vectors given are v = [2, 3] and w = [4, 1].

In 2D, the cross product magnitude (which gives the area of the parallelogram) can be calculated using the formula:

Area = |v x w| = |v||w|sin(θ)

where |v| and |w| are the magnitudes of v and w, and θ is the angle between them.

However, since we are in 2D, we can use a simplified version of the cross product, which is:

Area = |v x w| = |v1w2 - v2w1|

where v1, v2 are the components of vector v and w1, w2 are the components of vector w.

Substituting the given vectors into the formula, we get:

Area = |21 - 34| = |-10| = 10 square units.

So, the area of the parallelogram defined by v = [2, 3] and w = [4, 1] is 10 square units.