**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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