Matrix Transformation

It’s a subset of Linear transformation, just with higher 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 multiplicationgives you another Matrix, but a SHRINK-SIZED Matrix.

In General:
To multiply an m×n matrix by an n×p matrix, the ns 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.

Reflection of Shapes