Tutorial Week 5

Gaussian Elimination and Number of Solutions

Q1: Find the solutions to the system of equations \(\begin{cases} 2x + 4x^2 + 8x^3 - 4 = 0 \\ x + 2x^2 + 4x^3 = 2 \\ x + x^2 + x^3 = 1 \end{cases}\)

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Homogeneous Systems

Q2: Solve the following homogeneous system and classify the solution as trivial or non-trivial \(\begin{cases} 2x + 2y = 0 \\ 5x + y = 0 \end{cases}\)

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Q3: Solve the following homogeneous system and classify the solution as trivial or non-trivial \(\begin{cases} 2x + 2y = 0 \\ -x - y = 0 \end{cases}\)

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Midterm Review

Q4: If \(ABC^TCB^T\) produces a \(3 \times 2\) matrix and \((CB)^T\) produces a \(2 \times 6\) matrix, what are the dimensions of \(A\), \(B\), and \(C\)?

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