Question

Write the system in matrix form.

$\left|\begin{array}{c}x+2y+3z=1\\ 4x+5y+6z=4\\ 7x+8y+9z=9\\ \end{array}\right|$

Short answer

The matrix form

$$\begin{gathered} A\overrightarrow{x}=\overrightarrow{b}is \\ \left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}1\\ 4\\ 9\end{array}\right] \end{gathered}$$

Step-by-step solution

Step 1:

The matrix of the coefficients a are

$A=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$

The matrix with the variables is-

$\overrightarrow{x}=\left[\begin{array}{c}x\\ y\\ z\end{array}\right]$

The matrix of constants is

$\left[\begin{array}{c}1\\ 4\\ 9\end{array}\right]$

Hence, the matrix form

$$\begin{gathered} A\overrightarrow{x}=\overrightarrow{b}is \\ \left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}1\\ 4\\ 9\end{array}\right] \end{gathered}$$

Final answer:

The matrix form

$$\begin{gathered} A\overrightarrow{x}=\overrightarrow{b}is \\ \left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}1\\ 4\\ 9\end{array}\right] \end{gathered}$$