 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2021/8/c/solution

dim (U + V) + dim (U \cap V) = 4.

Since the sum lies in

R^{3}

and each plane has dimension two, the possibilities are

(dim (U + V), dim (U \cap V)) = (2, 2) or (3, 1) .

The first case means the planes coincide; two distinct planes through the origin intersect in a line.

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