How to determine eigenvalues and eigenvectors?

I have two matrices for example A and B. A=[3,9;3,5] and B=[2,0;0,8].

They are part of an eigenvalue problem of the form: (A-(lambda)B)x=0.

How do I find the eigenvalues and vectors using matlab? Please solve this problem using values and sharee the code from your monitor if possible.

Answer 1

[Bruno Luong]

A=[3,9;3,5]

A = 2×2

3 9 3 5

B=[2,0;0,8]

B = 2×2

2 0 0 8

[V lambda] = eig(A,B,'vector')

V = 2×2

1.0000 -1.0000 0.2074 0.4018

lambda = 2×1

2.4332 -0.3082

% here is the first eigen vector with lambda(1) the corresponfing eigen
% value
x1 = V(:,1)

x1 = 2×1

1.0000 0.2074

(A - lambda(1)*B)*x1 % small but not 0 due to finite precision floating point

ans = 2×1

1.0e-15 * 0.2220 -0.4441

% second eigen vector and second eigen value lambda(2)
x2 = V(:,2)

x2 = 2×1

-1.0000 0.4018

(A - lambda(2)*B)*x2 % small but not 0 due to finite precision floating point

ans = 2×1

1.0e-15 * 0.8882 0.4441

Answer 2

[Abderrahim. B]

Use eig

A = [3,9;3,5];
[eVecs, eVals] = eig(A) 

eVecs = 2×2

-0.9026 -0.8196 0.4304 -0.5729

eVals = 2×2

-1.2915 0 0 9.2915

Eigenvalues are the diagonal elements of eVals. To get them use diag

eValues = diag(eVals)

eValues = 2×1

-1.2915 9.2915

Answer 3

[Chunru]

% doc eig for more details
A=[3,9;3,5] 

A = 2×2

3 9 3 5

B=[2,0;0,8]

B = 2×2

2 0 0 8

[vA, dA] = eig(A)

vA = 2×2

-0.9026 -0.8196 0.4304 -0.5729

dA = 2×2

-1.2915 0 0 9.2915

[vB, dB] = eig(B)

vB = 2×2

1 0 0 1

dB = 2×2

2 0 0 8