Onstruct a 3x3 matrix A that has eigenvalues

[esoon87]

2. Construct a 3x3 matrix A that has eigenvalues 1, 2, and 4 with the associated eigenvectors [1 1 2]T, [2 1 -2]T and [2 2 1]T, respectively.

[Hint: use P-1AP = K, where K is the diagonal matrix]


hlp me... pls guild me to the step reli no idea how to do it

 

[Mark44]

P is the matrix whose columns are the eigenvectors you are given, and P^-1 is the inverse of this matrix. K is a diagonal matrix whose entries are the eigenvalues. Can you put these ideas together and figure out what A needs to be?