Final answer:
To match each system of equations to its solution represented by an augmented matrix, you need to understand how to convert a system of equations into an augmented matrix and then use row operations to solve the system.
Step-by-step explanation:
To match each system of equations to its solution represented by an augmented matrix, you need to understand how to convert a system of equations into an augmented matrix and then use row operations to solve the system. Here's a step-by-step explanation:
- Write down the system of equations.
- Arrange the coefficients of the variables into a matrix called the coefficient matrix.
- Write the constants on the right side of the equation and form a column vector called the constant matrix.
- Combine the coefficient matrix and the constant matrix to form an augmented matrix.
- Perform row operations to transform the augmented matrix into reduced row-echelon form.
- Read off the solutions from the reduced row-echelon form of the augmented matrix.