## Related questions with answers

Write each of the following systems of equation as a single matrix equation. See the earlier example.

$\left\{\begin{array}{l}x_3=x_2 \\ x_2=x_1 \\ x_1=x_3\end{array}\right.$

Solution

VerifiedGiven equations:

$\begin{equation*} x_3=x_2 \end{equation*}$

$\begin{equation*} x_2=x_1 \end{equation*}$

$\begin{equation*} x_1=x_3 \end{equation*}$

Rearrange the given equations in alphabetical order of the variables and the constants on the other side of the equation. If a certain variable is absent in an equation, write it with the coefficient of $0$ to be later incorporated in the matrix, therefore: Equation 1 becomes:

$\begin{equation*} 0x_1-x_2+x_3=0 \end{equation*}$

Equation 2 becomes:

$\begin{equation*} x_1-x_2+0x_3=0 \end{equation*}$

Equation 3 becomes:

$\begin{equation*} x_1+0x_2-x_3=0 \end{equation*}$

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