 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-2/3/a/solution

Move the right-hand side to the left. The resulting homogeneous linear system has coefficient matrix

(- 2 1 1 b - 2) .

A nonzero solution exists exactly when its determinant vanishes:

(- 2) (b - 2) - 1 = 0 .

Here the upper-left entry of the original matrix is

- 1

, as verified in the original PDF; that entry is corrupted in the local OCR.

 New to topics? Read the docs here!