Understanding Linear Transformations and Transformation Matrices

A way to find the inverse of a vector

A method to add vectors together

A mapping of vectors to another set of vectors

A process that scales vectors by a constant factor

Vector (1, 1, 1)

Vector (0, 0, 0)

Vector (1, 0, 0)

Vector (2, 2, 2)

As vector e3

As vector e1

As vector e4

As vector e2

It is used to calculate the inverse of a matrix

It helps in finding the determinant of a matrix

It determines the transformation matrix

It is used to solve linear equations

Transformation of vector e1

Transformation of vector e3

Transformation of vector e2

Transformation of vector e4

Vector (4, -4, 5)

Vector (5, -2, 5)

Vector (0, 2, 1)

Vector (1, 0, 0)

Transformation of vector e1

Transformation of vector e2

Transformation of vector e3

Transformation of vector e4

Vector (1, 0, 0)

Vector (0, 2, 1)

Vector (5, -2, 5)

Vector (4, -4, 5)

Four

Three

Two

One

To find the inverse of a vector

To map vectors to another set of vectors

To scale vectors by a constant factor

To add vectors together