Find the solution set to the following system of three linear equations in three unknowns over C by first placing its augmented matrix into RREF.
how would you do this question?
$$ix_1+ x_2 − x_3 = 0$$
$$−ix_2 + x_3 = 1$$
$$x_1 + x_2 − 2x_3 = 0$$
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$\begingroup$ how do you work with the i in the matrix $\endgroup$– akakaaOct 5, 2015 at 18:03
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$\begingroup$ Since your matrix is over $\mathbb{C}$, $i$ is treated like any other number. The exact same rules apply if you were working in $\mathbb{R}$. $\endgroup$– 9301293Oct 6, 2015 at 3:39
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1 Answer
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HINT: We create that matrix as follows,
$$ix_1+ x_2 − x_3 = 0$$
$$−ix_2 + x_3 = 1$$
$$x_1 + x_2 − 2x_3 = 0$$
$$ \Rightarrow \begin{bmatrix} i & 1 & -1 \\ -i & 1 & -1 \\ 1 & 1 & -2 \end{bmatrix} $$