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Problem 1

# Write the augmented matrix corresponding to each system of equations. $$\begin{array}{l} 2 x-3 y=7 \\ 3 x+y=4 \end{array}$$

Expert verified
The augmented matrix corresponding to the given system of linear equations $$\begin{array}{l} 2 x-3 y=7 \\ 3 x+y=4 \end{array}$$ is: $$\begin{bmatrix} 2 & -3 & 7 \\ 3 & 1 & 4 \\ \end{bmatrix}$$
See the step by step solution

## Step 1: Identify coefficients and constants

From the given system of equations $$\begin{array}{l} 2 x-3 y=7 \\ 3 x+y=4 \end{array}$$ The coefficients of x and y in the first equation are 2 and -3, respectively, and the constant term is 7. In the second equation, the coefficients of x and y are 3 and 1, respectively, and the constant term is 4. Step 2: Write the augmented matrix

## Step 2: Write the augmented matrix

Now we can write the augmented matrix corresponding to the given system of equations. The augmented matrix will have two rows (one for each equation) and three columns (one for each coefficient and one for the constant term). The matrix will look like this: $$\begin{bmatrix} 2 & -3 & 7 \\ 3 & 1 & 4 \\ \end{bmatrix}$$ The first row contains the coefficients and constant term of the first equation (2, -3, 7), and the second row contains the coefficients and constant term of the second equation (3, 1, 4).

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