 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2013/digital-systems-linear-algebra-introduction-to-formal-proof/4/e/solution

det B = (1 - t^{2})^{3} .

Consequently

B is not invertible exactly when t = 1 or t = - 1.

t = 1

, all four rows are equal. At

t = - 1

, successive rows alternate between one row and its negative. In either case the matrix rank is one, confirming the vanishing determinant.

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