im really struggling with this problem, i keep getting so far and then hitting a brick wall,
the question asks: diagonalise the matrix B=
[0 1 1]
[0 2 2]
[0 0 3]
in other words find an invertible matrix P and a diagonal matrix D so P'BP=D where P'= P inverse
can anybody please help, as i am really struggling!! thank you
thanks for your help, however the problem there is so far ive found 2 different sets of eigenvalues, and i cannot find corresponding eigenvectors for either set. this is really important i get this right, my next year at university rests on ensuring answers to problems like these are correct.
do you mean the polynomial I found, - lambda cubed + 5lambda squared - 6lambda. (sorry i couldnt find the symbols)
however i have also read that for a triangular square matrix the eigenvalues are the diagonal values?
i then cannot find the eigenvectors?! ive been attempting this question for a number of days now, please help.
so the eigenvalues are 0, 2 and 3.
I didn't know that but that's right.however i have also read that for a triangular square matrix the eigenvalues are the diagonal values?
Let's find the eigenvector whose corresponding eigenvalue is 2.i then cannot find the eigenvectors?! ive been attempting this question for a number of days now, please help.
We know that thus we have to solve
From (3) we get that , (2) is useless (0=0) and (1) tells us that so for . We can, for example, choose to get .
From (3) we get that , from (2) and (1) that . As there is no condition on , the solutions are the vectors for . If you choose, for example, , you get a non-zero vector.
No, it does not matter.I have the eigenvector for 3. When I then place the 3 eigenvectors into matrix form does it matter which column I place each vector in?!