k 3
0 2
You are given the 2x2 matrix M= (k 3) , where k is not 2.
(0 2)
i)Find the eigenvalues of M, and the corresponding eigenvectos.
ii)Express M in the form UDU^(-1), where D is a diagonal matrix.
iii)Hence find the matrix M^n.
4 answers
thats the 2x2 matrix, i m really stuck
det [ A - L I] = 0
det [ k-L , 3 / 0 , 2-L ] = 0
(k-L)(2-L) - 3*0 = 0
2k - (2+k) L + L^2= 0
L = {(2+k) +/- sqrt (k^2-4k+4) } / 2 but sqrt(k^2-4k+4) = (k-2)
so
L = {k+2 +k-2}/2 = k
or
L = {k+2 -k+2}/2 = 2
eigenvalues are k and 2
det [ k-L , 3 / 0 , 2-L ] = 0
(k-L)(2-L) - 3*0 = 0
2k - (2+k) L + L^2= 0
L = {(2+k) +/- sqrt (k^2-4k+4) } / 2 but sqrt(k^2-4k+4) = (k-2)
so
L = {k+2 +k-2}/2 = k
or
L = {k+2 -k+2}/2 = 2
eigenvalues are k and 2
suggest this:
https://www.youtube.com/watch?v=IdsV0RaC9jM
https://www.youtube.com/watch?v=IdsV0RaC9jM
2 answers