Scalar Times Matrix: Every Cell Scales
Multiply a matrix by a number — every entry gets multiplied.
Equation
y = 1 * x
Graph
Table
| x | y |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 8 |
| 9 | 9 |
What this lesson covers
What you do
You shape the function y = k * x and watch the graph answer.
Challenges to clear
- Slide k to 3: an entry of 2 becomes 6 — EVERY cell scales.
- And an entry of 4 becomes 12 — same multiplier everywhere.
- Scale the matrix twice over. The first scalar is 2 — slide m there.
- Now the second: an entry of 3 must end on 24. Two scalars applied in turn simply multiply together.
Check yourself
For a 2x2 matrix A and scalar k, the entry (kA)_ij is:
If k=-1, what happens to the matrix entries?
- k * a_ij — the scalar distributes over every cell. — correct
- k + a_ij — addition, not multiplication.
- Only the diagonal entries scale; off-diagonal stay the same.
- a_ij^k — the scalar acts as an exponent.
- They become their additive inverses (signs flip). — correct
- They become zero.
- They remain unchanged.
- They become positive regardless of original sign.
Think about it
- If the scalar k is 3, what happens to a matrix entry that was 2?