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Cogito

Linear Algebra · Chapter 2 · Lesson 2

Practice Worksheet

Gaussian Elimination

Clear out entries until the answer is obvious.

12 problems · about 24 minutes · A-REI.C.6, A-REI.C.8

NameDate

Figure — use these to answer the problems

Row reduce this by hand and then set the entries to match your result. A zero below the first pivot means the column is cleared.
xy=1273111
row 1, x1
row 1, y2
row 1, constant7
row 2, x3
row 2, y1
row 2, constant11
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. A row reads [0, 5 | 20]. What is y?

    Answer

  2. What shape is Gaussian elimination aiming for?

    • A staircase of zeros below the pivots.
    • Every entry equal to zero.

  3. A row reads [0, 3 | 9]. What is y?

    Answer

  4. A row reads [0, −2 | 8]. What is y?

    Answer

  5. Row 1 is [1, 1 | 10] and y = 4. What is x?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Clearing the entry 5 below a pivot of 1. What multiple of the pivot row is subtracted?

    Answer

  2. In reduced row echelon form, what is every pivot scaled to?

    Answer

  3. A 3 by 3 system fully reduced. How many pivots does it have if it has a unique solution?

    Answer

Stretch Yourself

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

4 problems

  1. Order the steps of Gaussian elimination.

    Write 1 to 4 in the boxes to put these in order.

    • Choose a pivot in the first column
    • Clear every entry beneath that pivot
    • Move to the next column and repeat
    • Back-substitute from the bottom row upward

  2. A row reads [0, 1 | −6]. What is y?

    Answer

  3. The Bottom Row

    A reduced row reads [0, 4 | 12]. What is y?

    Answer

  4. The Substitution

    Row 1 reads [1, 2 | 7] and you know y = 2. What is x?

    Answer