Matrix Transformation
It’s a subset of
Linear transformation
, just withhigher dimension rules
&multiple points graph
multiplying together.
YOU BREAK THE RULE
IN TO DIFFERENT UNIT VECTORS i, j, k... AND BREAK THE GRAPH INTO DIFFERENT POINTS, AND APPLY EACH i, j, k RULES TO EACH POINT.
Size of Matrix multiplication
Unlike Vector multiplication
gives you only a number, Matrix multiplication
gives you another Matrix
, but a SHRINK-SIZED Matrix.
In General:
To multiply an m×n matrix
by an n×p matrix
, the n
s must be the same,
and the RESULT is an m×p matrix
.
Example: 3x2 Matrix with 2x2 Matrix
Solve:
- First we know it’s a 3x2 Matrix multiply a 2x2 Matrix, it’s valid, and the new Matrix’s size would be 3x2.
- And then we multiply each by each according to their dimension:
- We get the answer:
Example: 2x2 Matrix with 2x3 Matrix
Solve:
- It’s will get a 2x3 new Matrix (just for intuition), then we get the answer:
More examples
Refer to Symbolab the Online math solver, which offers answers of any matrices operation step by step.
Common Matrix Transformations
One single matrix to present the movement? Yes!
Refer to Math planet: Transformation using matrices
Rotation of Shapes
▶ Use the tool: Desmos Matrix Calculator
Example: Transform Graphs
Solve:
- Just to list all points of this graph:
(-4,8), (-8,-4), (-4,-4), (0,4)
- Arrange points to a Matrix:
- Apply the Matrix R to the Graph’s matrix. Do the math.