Eigenvalues and Eigenvectors Concepts

To find the inverse of a matrix

To determine the eigenvalues and eigenvectors of a matrix

To solve a system of linear equations

To calculate the determinant of a matrix

Gaussian elimination

Matrix inversion

Determinant method

Row reduction

Two eigenvalues

No eigenvalues

Three eigenvalues

A single eigenvalue

Using a constant

Using a polynomial

Using a variable 't'

Using a matrix

x2 = 3x3

x2 = x3

x2 = 2x3

x2 = -x3

Finding the inverse of the matrix

Solving a system of equations

Normalizing the eigenvectors to find unit eigenvectors

Calculating the determinant

√2

√3

√5

√6

(0, 0, 1)

(0, 1, 0)

(1, 0, 0)

(-1, 0, 0)

By dividing the eigenvector by its magnitude

By subtracting the eigenvector components

By adding the eigenvector components

By multiplying the eigenvector by a constant

√49

√69

√81

√100