RREF-in' problems

[peacefreak77]

I was trying to review some linear algebra stuff today, and I encountered a problem.

I was doing multivariable DDS a(n + 1) = 2a(n) + b(n) and b(n + 1) = 4a(n) + 3b(n).

I got eigenvalues of 4.56 and 0.438. However, when I plugged them into the equation:

. . .0 = (R - lambda*I)A

...I ended up, for the first lambda for example, with:

. . .[[-2.56, 1][4, -1.56]]*[[a(n)][b(n)]] = [[0][0]]

When I solved that manually I got:

. . .[[a(n)][b(n)]] = [[1][2.56]]

But when I tried to RREF it on my calculator I got:

. . .[[a(n)][b(n)]] = [[0][0]]

...which I am fairly certain is incorrect.

What am I doing wrong in entering the problem into my calculator? (Or in doing it by hand I suppose)?

 

[JakeD]

I was trying to review some linear algebra stuff today, and I encountered a problem. I was doing multivariable DDS a(n+1)=2a(n)+b(n) and b(n+1)=4a(n)+3b(n). I got eigenvalues of 4.56 and .438. However, when I plugged them into the equation 0=(R-lambda*I)A I ended up, for the first lambda for example, with [[-2.56, 1][4, -1.56]]*[[a(n)][b(n)]]=[[0][0]]. When I solved that manually I got [[a(n)][b(n)]]=[[1][2.56]] but when I tried to RREF it on my calculator I got [[a(n)][b(n)]]=[[0][0]], which I am fairly certain is incorrect.

What am I doing wrong in entering the problem into my calculator? (Or in doing it by hand I suppose)?

You're not working with enough precision: 2.56 * 1.56 = 3.9936, so [4,-1.56]*[1,2.56] = .0064, not zero.