Systems and Augmented Matrices

Strip away the letters and keep the numbers.

12 problems · about 22 minutes · A-REI.C.6, A-REI.C.8

NameDate

Figure — use these to answer the problems

The rule separates the coefficients from the constants. Change any entry and read off the equation it now describes.

row 1, x2

row 1, y1

row 1, constant8

row 2, x1

row 2, y3

row 2, constant9

Figure 1

Straightforward practice. Get the method working first.

5 problems

5x − 3y = 11. What is the coefficient of y?
Answer
2
What does the vertical rule in an augmented matrix mark?
- The split between the coefficients and the constants.
- Nothing; it is decoration.
x + 5y = 7. What goes in the constant column?
Answer
x + 5y = 7. What is the coefficient of x?
Answer
2x − y = 0. What is the coefficient of y?
Answer

The same ideas with more to keep track of.

3 problems

A system of 2 equations in 2 unknowns. How many columns does the augmented matrix have?
Answer
How many legal row operations are there?
Answer
Multiplying a row by 0. Is that legal? 1 yes, 0 no.
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

Sort each move by whether it is a legal row operation.
Write each item under the heading it belongs to: Swap two rows · Multiply a row by 5 · Multiply a row by 0 · Add twice row 1 to row 2
Legal
Not allowed
Do row operations change the solution set? 1 yes, 0 no.
Answer
The Reading
The row [4, −2 | 10] stands for 4x − 2y = 10. What is the coefficient of y?
Answer
The Size
A system of 3 equations in 4 unknowns. How many columns does the augmented matrix have?
Answer