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Cogito

Precalculus · Chapter 6 · Lesson 1

Practice Worksheet

Matrix Operations

A grid of numbers that acts like a single object.

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

NameDate

Figure — use these to answer the problems

Change the entries and watch the product recompute. Each output entry is one row against one column.
2134
Top left2
Top right1
Bottom left3
Bottom right4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Row (3, 1) against column (2, 4). What is the entry?

    Answer

  2. Is AB always equal to BA for matrices?

    • No, and one may not even be defined.
    • Yes, multiplication always commutes.

  3. A 3×5 matrix has how many entries?

    Answer

  4. Row (2, 3) against column (4, 1). What is the entry?

    Answer

  5. A 4×2 times a 2×3. How many rows does the result have?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Scale [[1, 2], [3, 4]] by 5. What is the bottom-right entry?

    Answer

  2. Add [[1, 2], [3, 4]] and [[5, 5], [5, 5]]. What is the top-left entry?

    Answer

  3. Can a 2×3 be added to a 3×2? Enter 1 for yes, 0 for no.

    Answer

Stretch Yourself

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

4 problems

  1. Which products are defined?

    • 2×3 times 3×2
    • 4×1 times 1×4
    • 2×3 times 2×3
    • 3×2 times 3×2
    • Tick every box that applies.

  2. Row (0, 5) against column (6, 2). What is the entry?

    Answer

  3. The Size

    A 2×3 matrix times a 3×4 matrix. How many columns does the result have?

    Answer

  4. The Entry

    Row (1, 2) against column (5, 7). What is the entry?

    Answer