**Eigenvalues of 2 x 2 Matrices**

Many graphing calculators that do not have CAS (computer algebraic systems) do not have eigenvalues and eigenvector functions.

The program for the Casio Prizm gives eigenvalues. The TI-84+ program gives both eigenvalues and eigenvectors.

For the HP 39gii has the functions EIGENVAL and EIGENVV for eigenvalues and eigenvectors, respectively.

Example:

A = [[2, 7][-3, 9]]

Eigenvalues: ≈ 5.5 ± 2.9580i

Casio Prizm:

Eigenvalues of a 2 × 2 Matrix

EIGEN2 - 136 Bytes

a+bi

"2 × 2 MATRIX:"? → Mat A

Mat A[1,1] + Mat A[2,2] → T

Det Mat A→ D

(T+√(T^2-4D))÷2 → R ◢

(T-√(T^2-4D))÷2 → S ◢

"λS STORED IN R,S"

TI-84+:

EIGEN2

Eigenvalues of 2 × 2 matrices - Approximately 280 bytes

Bonus! A pair of eigenvectors are given

5/15/2011

a+bi

Input "2 X 2 MATRIX:", [J]

[J](1,1) + [J](2,2) → T

det([J]) → D

(T + √(T^2 - 4D))/2 → U

(T - √(T^2 - 4D))/2 → V

Disp "EIGENVAL. U"

Pause U

(U - [J](1,1)) / [J](1,2) → A

√(1 + A^2)⁻¹ * [[1][A]] → [H]

Disp "EIGENVEC. [H]"

Pause [H]

(V - [J](1,1)) / [J](1,2) → B

√(1 + B^2)⁻¹ * [[1][B]] → [I]

Disp "EIGENVAL. V"

Pause V

Disp "EIGENVECT. [I]"

Pause [I]

This blog is property of Edward Shore. 2012

Hi Edward, i followed your guide in programming my TI-84+ to calculate the eigenvects & vals but upon executing the program, it always reflect ERR:UNDEFINED. any idea what might be the cause of problem? Any help is greatly appreciated!!

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