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Cogito

Precalculus · Chapter 6 · Lesson 3

Practice Worksheet

Solving Systems with Matrices

Write a whole system as one equation.

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

NameDate

Figure — use these to answer the problems

This is the coefficient matrix of a system. When its determinant is zero, no unique solution exists.
2113
  • Determinant of M5
Coefficient of x, equation 12
Coefficient of y, equation 11
Coefficient of x, equation 21
Coefficient of y, equation 23
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Determinant of A is 3, and the x-determinant is 12. What is x?

    Answer

  2. A coefficient matrix has determinant zero. What does that say about the system?

    • It has no unique solution.
    • Both unknowns equal zero.

  3. Coefficient matrix [[1, 2], [3, 4]]. Determinant?

    Answer

  4. Coefficient matrix [[2, 4], [1, 2]]. Determinant?

    Answer

  5. With that zero determinant, is there a unique solution? 1 for yes, 0 for no.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. In AX = B, what does X hold?

    • The unknowns.
    • The constants.

  2. Determinant of A is 5, and the x-determinant is 20. What is x?

    Answer

  3. Determinant of A is 4, and the y-determinant is −8. What is y?

    Answer

Stretch Yourself

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

4 problems

  1. Put the matrix solving method in order.

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

    • Write the system as AX = B.
    • Compute the determinant of A.
    • Confirm it is not zero.
    • Multiply both sides on the left by A⁻¹.

  2. x + y = 7 and x − y = 1. What is x?

    Answer

  3. The Determinant

    A system has coefficient matrix [[3, 2], [1, 4]]. What is its determinant?

    Answer

  4. The Tickets

    Adult tickets cost $8 and child tickets $5. 10 tickets cost $68. How many adult tickets were sold?

    Answer