 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2/11/b/iii/solution

In the nonsingular case the unique solution is

x = a + \frac{b \cdot a}{1 - b \cdot c} c, b \cdot c \neq = 1 .

Geometrically this is a single selected point of the straight line through

a

parallel to

c

When

b \cdot c = 1

and

b \cdot a = 0

a + λ c

. The remaining case has empty solution set. In matrix terms the equation is

(I - c b^{T}) x = a

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