Using MATLAB solve this

Experiment with MATLAB Dtermine the behaviour of the matix sequence A^k aproaches to infinity for each of following matrices .. A=(1/2 1/3; 1/4 1/5) B= ( 1 -1 0; 0 1 -1; -1 0 1).

Answer 1

[Chunru]

% For matrix A;  (Try it out yourself with matric B)
A=[1/2 1/3; 1/4 1/5];
Ak = A;
for k=2:20
    Ak = Ak*A
end

Ak = 2×2

0.3333 0.2333 0.1750 0.1233

Ak = 2×2

0.2250 0.1578 0.1183 0.0830

Ak = 2×2

0.1519 0.1066 0.0799 0.0560

Ak = 2×2

0.1026 0.0720 0.0540 0.0378

Ak = 2×2

0.0693 0.0486 0.0364 0.0256

Ak = 2×2

0.0468 0.0328 0.0246 0.0173

Ak = 2×2

0.0316 0.0222 0.0166 0.0117

Ak = 2×2

0.0213 0.0150 0.0112 0.0079

Ak = 2×2

0.0144 0.0101 0.0076 0.0053

Ak = 2×2

0.0097 0.0068 0.0051 0.0036

Ak = 2×2

0.0066 0.0046 0.0035 0.0024

Ak = 2×2

0.0044 0.0031 0.0023 0.0016

Ak = 2×2

0.0030 0.0021 0.0016 0.0011

Ak = 2×2

0.0020 0.0014 0.0011 0.0007

Ak = 2×2

0.0014 0.0010 0.0007 0.0005

Ak = 2×2

1.0e+-3 * 0.9232 0.6474 0.4856 0.3405

Ak = 2×2

1.0e+-3 * 0.6235 0.4372 0.3279 0.2300

Ak = 2×2

1.0e+-3 * 0.4210 0.2953 0.2215 0.1553

Ak = 2×2

1.0e+-3 * 0.2843 0.1994 0.1496 0.1049

[Rik]

@Chunru, why did you provide the solution to a homework question? The OP didn't show any effort whatsoever and now you're rewarding laziness. (if they weren't lazy, they should have included at least an indication they tried something)