 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2014/digital-systems-linear-algebra-introduction-to-formal-proof/5/e/solution

The right-hand vector is in the column space, because

2 - 1 12 + 325 = 149 .

Consequently the linear system is consistent. A concrete solution is

x = (2, 0, 1, 0, 0)^{T} .

As a compatibility check, the original rows satisfy

r_{1} + 11 r_{2} - 5 r_{3} = 0

, and the right-hand entries satisfy the same relation

1 + 11 \cdot 4 - 5 \cdot 9 = 0

. There are infinitely many solutions, obtained by adding any vector in the null space to the displayed solution.

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