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

What this lesson teaches

The student adds, scales and multiplies matrices and states when each operation is defined.

A matrix is sized rows by columns, and addition needs identical sizes.
Multiplication takes rows against columns, and needs the inner dimensions to match.
AB and BA are generally different.

Straightforward practice. Get the method working first.

5 problems

Row (3, 1) against column (2, 4). What is the entry?
Answer 10
Why 10.
Is AB always equal to BA for matrices?
Answer No, and one may not even be defined.
Why Matrix multiplication is not commutative.
A 3×5 matrix has how many entries?
Answer 15
Why Rows times columns.
Row (2, 3) against column (4, 1). What is the entry?
Answer 11
Why 8 + 3.
A 4×2 times a 2×3. How many rows does the result have?
Answer 4
Why The first matrix supplies the rows.

The same ideas with more to keep track of.

3 problems

Scale [[1, 2], [3, 4]] by 5. What is the bottom-right entry?
Answer 20
Why 5 × 4.
Add [[1, 2], [3, 4]] and [[5, 5], [5, 5]]. What is the top-left entry?
Answer 6
Why 1 + 5.
Can a 2×3 be added to a 3×2? Enter 1 for yes, 0 for no.
Answer 0
Why Addition needs identical sizes.

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

4 problems

Which products are defined?
Answer 2×3 times 3×2; 4×1 times 1×4
Why The inner dimensions must match.
Row (0, 5) against column (6, 2). What is the entry?
Answer 10
Why 0 + 10.
The Size: A 2×3 matrix times a 3×4 matrix. How many columns does the result have?
Answer 4
Why 4.
The Entry: Row (1, 2) against column (5, 7). What is the entry?
Answer 19
Why 19.