Exercise 12

Intersection and sum in R⁴

In $R^{4}$ consider

U : x_{1} + x_{2} + x_{3} + x_{4} = 0, W = ⟨(1, - 1, 0, 0), (1, 1, 1, 1), (0, 0, 1, - 1)⟩ .

Find a basis of $U \cap W$ and the dimension of $U + W$ .

The full solution of this exercise is in the unlocked version.