Solve the following system of linear equation by Gaussian Elimination Method. x^1 + 2x^2 – x^3 = 1, 3x^1 – 2x^2 + 2x^3 = 2, 7x^1 – 2x^2 + 3x^3 = 5.

asked by guest
on Nov 15, 2024 at 7:55 am



You asked:

Solve the system of equations:\[\begin{aligned}{x}^{1} + 2 \cdot {x}^{2} - {x}^{3} &= 1\\3 \cdot {x}^{1} - 2 \cdot {x}^{2} + 2 \cdot {x}^{3} &= 2\\7 \cdot {x}^{1} - 2 \cdot {x}^{2} + 3 \cdot {x}^{3} &= 5\end{aligned}\]

MathBot Answer:

The system of equations has \(3\) solutions.

\[x = - \frac{59}{81 \sqrt[3]{\frac{853}{1458} + \frac{5 \sqrt{85}}{54}}} + \frac{2}{9} + \sqrt[3]{\frac{853}{1458} + \frac{5 \sqrt{85}}{54}}\]\[x = - \frac{\sqrt[3]{\frac{853}{1458} + \frac{5 \sqrt{85}}{54}}}{2} + \frac{2}{9} + \frac{59}{162 \sqrt[3]{\frac{853}{1458} + \frac{5 \sqrt{85}}{54}}} + i \left(\frac{59 \sqrt{3}}{162 \sqrt[3]{\frac{853}{1458} + \frac{5 \sqrt{85}}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{853}{1458} + \frac{5 \sqrt{85}}{54}}}{2}\right)\]\[x = - \frac{\sqrt[3]{\frac{853}{1458} + \frac{5 \sqrt{85}}{54}}}{2} + \frac{2}{9} + \frac{59}{162 \sqrt[3]{\frac{853}{1458} + \frac{5 \sqrt{85}}{54}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{853}{1458} + \frac{5 \sqrt{85}}{54}}}{2} - \frac{59 \sqrt{3}}{162 \sqrt[3]{\frac{853}{1458} + \frac{5 \sqrt{85}}{54}}}\right)\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

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