Question

name the parts of the matrix equation in order. \\(\

$$\begin{bmatrix}2 & 1 \\\\ 7 & 3\\end{bmatrix}$$

• \

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

= \

$$\begin{bmatrix}-53 \\\\ -22\\end{bmatrix}$$

\\) options: constant matrix variable matrix = coefficient matrix; coefficient matrix constant matrix = variable matrix; constant matrix coefficient matrix = variable matrix; coefficient matrix variable matrix = constant matrix

Explanation:

Step1: Identify Coefficient Matrix

The coefficient matrix contains the coefficients of the variables in the system of equations. From the matrix equation

$$\begin{bmatrix}2 & 1\\7 & 3\end{bmatrix}*\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-53\\-22\end{bmatrix}$$

, the matrix with the coefficients of \(x\) and \(y\) is

$$\begin{bmatrix}2 & 1\\7 & 3\end{bmatrix}$$

, so this is the coefficient matrix.

Step2: Identify Variable Matrix

The variable matrix contains the variables of the system. Here, the matrix with \(x\) and \(y\) is

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

, so this is the variable matrix.

Step3: Identify Constant Matrix

The constant matrix contains the constant terms on the right - hand side of the equation. In the given equation, the matrix

$$\begin{bmatrix}-53\\-22\end{bmatrix}$$

has the constant values, so this is the constant matrix.

Answer:

Coefficient matrix:

$$\begin{bmatrix}2 & 1\\7 & 3\end{bmatrix}$$

, Variable matrix:

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

, Constant matrix:

$$\begin{bmatrix}-53\\-22\end{bmatrix}$$