Addition of two vectors. Given the vectors

a) Graph very accurately their addition, that is (a1 + a2), and verify that the resulting vector is the main diagonal of a parallelogram constructed using the two vectors (a1, a2) as sides of the parallelogram.

b) Verify (geometrically) that

Therefore, any system of two equations and two columns corresponds to the addition of two vectors.

c) Generalization. Graphically, verify that the system of two equations and two unknowns

has solution x∗
1 = 1 and x∗
2 = 1. This means that finding the solution of systems of equations corresponds to constructing the parallelogram using the a1, a2 vectors as sides and whose main diagonal is the sum of those vectors.

a 3 H = [-1]