Module 7: Connecting Algebra and Geometry by Natalie Wilson

Vocabulary

wilsonn1225 — 2017-03-15 17:58:32 UTC

determinant: a useful value that can be determined from a square matrix.

Multiplicative Inverse Matrix: A matrix that when multiplied by the original matrix the product is the multiplicative identity matrix.

Multiplicative Inverse Matrix: A matrix that when multiplied by a matrix results in the same matrix.
[1 0]
[0 1]

Additive Inverse Matrix: A matrix that when added to the original matrix the resulting sum is the additive identity.

Additive Identity Matrix: A matrix that when added to another matrix the resulting sum is the same matrix.
[0 0]
[0 0]

Vector: a quantity that has both magnitude and direction

Magnitude: the distance moved

Direction: the direction in which the object is moved.

Vector Notation

wilsonn1225 — 2017-03-15 18:35:58 UTC

A vector that goes up 7 and right 8 is written as:
<8 , 7>
with the x-movement listed first and the y-movement listed second.

Finding the Determinant of the Matrix

wilsonn1225 — 2017-03-15 18:38:47 UTC

The determinant of a matrix is ad-bc, when:

[a c]
[b d]

Solving a System of Equations Using an Inverse Matrix

wilsonn1225 — 2017-03-15 18:40:00 UTC

Finding the Multiplicative Inverse of a Matrix

wilsonn1225 — 2017-03-15 18:40:07 UTC

Finding the Additive Inverse of a Matrix

wilsonn1225 — 2017-03-15 18:41:45 UTC

The additive inverse of a matrix places the opposite of a number in the slot the number is in.

[1 2]
[3 4]

Additive inverse:

[-1 -2]
[-3 -4]

Adding Vectors

wilsonn1225 — 2017-03-15 18:41:55 UTC

Writing Quadrilaterals as a Matrix

wilsonn1225 — 2017-03-15 18:42:34 UTC

When writing quadrilaterals as a matrix, you take the coordinates of the point and put them in a matrix, where one row or column is a ordered pair and each row or column is an x or y value.

Quadrilateral ABCD
a= (9, 5) b= (10, 2) c= (4, -1) d= (-2, -2)

[9 10 4 -2]
[5 2 -1 -2

Applying Transformations to Matrices

wilsonn1225 — 2017-03-15 18:43:05 UTC

To apply transformations to matrices, you multiply them by the following matrices:

Reflection across the Y-axis:
[-1 0]
[0 1]

Reflection across the X-axis:
[1 0]
[0 -1]

Rotation 90° counterclockwise about the origin:
[0 -1]
[1 0]

Rotation 180° about the origin:
[-1 0]
[0 -1]

Rotation 270° counterclockwise about the origin:
[0 1]
[-1 0]

Transformation Notation

wilsonn1225 — 2017-03-15 18:51:10 UTC

Transformation notation describes one equation in terms of another.

f(x) = 5x - 2
g(x) = f(x) - 5

g(x) is described in transformation notation because it is described in terms of f(x).