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Cogito

Precalculus · Chapter 6 · Lesson 2

Practice Worksheet

Determinants and Inverse Matrices

One number decides whether a matrix can be undone.

12 problems · about 22 minutes · TEKS P.3.G

NameDate

Figure — use these to answer the problems

Set the entries so that ad equals bc. The determinant hits zero, and the matrix stops being invertible.
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 matrix is singular and has no inverse.
    • 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. [[2, 0], [0, 3]]. Determinant?

    Answer

  2. A determinant of 0 means an inverse exists? Enter 1 for yes, 0 for no.

    Answer

  3. A transformation has determinant 5. A shape of area 3 becomes what area?

    Answer

Stretch Yourself

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

4 problems

  1. Put the steps for finding a 2×2 inverse in order.

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

    • Compute the determinant, ad − bc.
    • Check that it is not zero.
    • Swap a and d, and negate b and c.
    • Divide every entry by the determinant.

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

    Answer

  3. The Determinant

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

    Answer

  4. The Singular One

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

    Answer