The calculator will find the eigenvalues and eigenvectors of the square
2x
2 matrix
[31−10−4], with steps shown.
Related calculator:
Characteristic Polynomial Calculator
Solution
Start from forming a new matrix by subtracting λ from the diagonal entries of the given matrix: [3−λ1−10−λ−4].
The determinant of the obtained matrix is (λ−1)(λ+2) (for steps, see determinant calculator).
Solve the equation (λ−1)(λ+2)=0.
The roots are λ1=1, λ2=−2 (for steps, see equation solver).
These are the eigenvalues.
Next, find the eigenvectors.
λ=1
[3−λ1−10−λ−4]=[21−10−5]
The null space of this matrix is {[51]} (for steps, see null space calculator).
This is the eigenvector.
λ=−2
[3−λ1−10−λ−4]=[51−10−2]
The null space of this matrix is {[21]} (for steps, see null space calculator).
This is the eigenvector.
Answer
Eigenvalue: 1A, multiplicity: 1A, eigenvector: [51]A.
Eigenvalue: −2A, multiplicity: 1A, eigenvector: [21]A.