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Cogito

AP Precalculus · Chapter 8 · Lesson 3

Practice Worksheet

Matrices as Transformations

A grid of numbers that moves the plane.

12 problems · about 22 minutes · AP Precalculus 4.10, 4.12, 4.13

NameDate

Figure — use these to answer the problems

Change the entries so that ad equals bc. The determinant hits zero and the transformation stops being reversible.
4264
  • Determinant of M4
Top left4
Top right2
Bottom left6
Bottom right4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. [[4, 1], [3, 2]]. What is the determinant?

    Answer

  2. What does a determinant of zero mean?

    • The transformation flattens the plane, so it cannot be undone.
    • The matrix is the identity.

  3. [[5, 2], [3, 4]]. Determinant?

    Answer

  4. [[1, 0], [0, 1]]. Determinant?

    Answer

  5. [[6, 3], [4, 2]]. Determinant?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Does that matrix have an inverse? 1 yes, 0 no.

    Answer

  2. Determinant 4 applied to a shape of area 7. New area?

    Answer

  3. Row (1, 2) against the vector (5, 7). What is the result?

    Answer

Stretch Yourself

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

4 problems

  1. Match each determinant value with what it means.

    Draw a line from each item on the left to its match on the right.

    • Determinant 1
    • Determinant 3
    • Determinant 0
    • Areas are unchanged
    • Areas are tripled
    • The plane collapses onto a line

  2. [[7, 3], [2, 1]]. Determinant?

    Answer

  3. The Determinant

    [[3, 1], [2, 4]]. What is the determinant?

    Answer

  4. The Area

    A shape of area 5 under a transformation with determinant 10. What is the new area?

    Answer