Vector: Matrix where n is 1, so there is only one row
A matrix is made up of rows and columns like a table
Rows: Horizontal, has “m” amount of rows
Columns: Vertical, has “n” amount of columns
Order of matrix: rows*columns
When m = n the matrix is said to be square
Matrices can be used to solve systems of equations (Gaussian Elimination):
Identity Matrix:
A Matrix with one diagonal of values of 1, which will give you the solutions on the right side
How a matrix can be simplified:
Matrix Operations:
Matrices have to be in the SAME order to be added or subtracted, and each component is added with the corresponding component in the other matrix
The order of the matrices in multiplication does matter and can give radically different answers
You also can’t multiply matrices of different sizes
Division technically doesn’t exist, but you can just multiply by the inverse.
The determinant: The volume of the scaling factor of the linear transformation.
It only works on square matrices like 2×2 and 3×3.
If the determinant is 0, then there is no solution.
Cramer’s Rule:
A super-easy way to get the x and y solution from a matrix using the determinant.
Where Ax just means the first column and Ay just means the second column, and it can also be used to find z.
How to find an easy inverse of a matrix:
Matrix Element:
Where two lines intersect on each other and have one value, like M(1,1) could be 3, if it’s in the top-left corner.
Minor of a matrix:
Making a smaller matrix, by deleting certain parts
Zero Matrix: A matrix where every component is 0
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