 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ib/paper-3/9e/a/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Row reduction of the matrices whose columns are the displayed spanning vectors gives

dim U = 3, dim W = 3.

Row-reducing the matrix formed from all six columns gives

dim (U + W) = 4.

dim (U \cap W) = dim U + dim W - dim (U + W) = 3 + 3 - 4 = 2 .

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