Question

express the equations \\(2x + y + z = 3\\), \\(5x - y + 4z = 2\\), and \\(4x - 3y + z = 1\\) as a matrix equation.

\\(\bigcirc\\) \\(\

$$\begin{bmatrix} 2 & 0 & 1 \\\\ 5 & -1 & 4 \\\\ 4 & -3 & 1 \\end{bmatrix}$$

\

$$\begin{bmatrix} x \\\\ y \\\\ z \\end{bmatrix}$$

= \

$$\begin{bmatrix} 3 \\\\ 2 \\\\ 1 \\end{bmatrix}$$

\\)

\\(\bigcirc\\) \\(\

$$\begin{bmatrix} 2 & 1 & 1 \\\\ 5 & -1 & 4 \\\\ 4 & -3 & 1 \\end{bmatrix}$$

\

$$\begin{bmatrix} x \\\\ y \\\\ z \\end{bmatrix}$$

= \

$$\begin{bmatrix} 3 \\\\ 2 \\\\ 1 \\end{bmatrix}$$

\\)

Explanation:

Identify the system of linear equations

Using the Coefficient Matrix knowledge point

$$
LATEXBLOCK0
$$

Extract the coefficient matrix

Using the Coefficient Matrix knowledge point

$$ A =
LATEXBLOCK1
$$

Formulate the matrix equation

Using the Solving Matrix Equations knowledge point

$$
LATEXBLOCK2

LATEXBLOCK3
=
LATEXBLOCK4
$$

Answer:

• (A) \(

$$\begin{bmatrix} 2 & 0 & 1 \\ 5 & -1 & 4 \\ 4 & -3 & 1 \end{bmatrix}$$

$$\begin{bmatrix} x \\ y \\ z \end{bmatrix}$$

=

$$\begin{bmatrix} 3 \\ 2 \\ 1 \end{bmatrix}$$

\)

• **(B) \(

$$\begin{bmatrix} 2 & 1 & 1 \\ 5 & -1 & 4 \\ 4 & -3 & 1 \end{bmatrix}$$

$$\begin{bmatrix} x \\ y \\ z \end{bmatrix}$$

=

$$\begin{bmatrix} 3 \\ 2 \\ 1 \end{bmatrix}$$

\) (Correct answer)**