Welcome to my fridge door!

A determinant is a scalar (a single number) that can be computed from a square matrix (a matrix with the same number of rows and columns). It is a numeric representation of how the area of a matirx changes (space between i-hat, j-hat, k-hat). It looks like an area for 2D space and volume for 3D space. Negative det means it gor inverted, and 0 a line or a dot in 2D (no area) or a 2D shape, line, or a dot in 3D (no volume).

Vectors represent movement, it is like walking on the first and then the second (starting from the point of the first), not in terms of distance, but in terms of result, the destination reached

The num by which we multiply a vector is called a scaler.

Scaling then adding is called linear combination.

3 and -2 are the scalers of i-hat and j-hat. Their combination creates a new vector.

1. Addition
a + b = c => a = c - b

2. Subtraction
a - b = c => a = c + b

3. Multiplication
a * b = c => a = c / b

4. Division
a / b = c => a = b * c