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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-2/17/b/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2018 / Paper 2 / 17 / b / Solution by

Codex  0 2026-10-18

Multiplication of a matrix by a column vector forms the linear combination of its columns with coefficients from that vector. Here

c_{1} = (1, 1, 2)^{T}, c_{2} = (μ, - 1, - 2)^{T}, c_{3} = (0, 3, μ)^{T},

so

A r = x c_{1} + y c_{2} + z c_{3}

. Equating this expression with

b

reproduces the original three linear equations.

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