diagonal matrix: is this matrix diagonalizable? explain.

[luckyc1423]

Is the matrix

. . .[ 1 1 1 ]
. . .[ 0 1 1 ]
. . .[ 0 0 0 ]

diagonalizable? Explain.

 

[pka]

The various problems you have listed here and elsewhere depend upon definitions.
You need to know that in many cases definitions vary with the textbooks.
You also need to lookup the definitions in your text.
In the present case, the answer is a straightforward application of the definition.

 

[Trenters4325]

First calculate the eigenvectors and eigenvalues of A using the method you learned in your next thread. Then put the eigenvectors into the columns of a new matrix P (your diagonalizing matrix) and find that (P^-1)(A)(P) is a diagonal matrix containing the eigenvalues on its diagonal. If all of that works (and it will iff the eigenvectors you find are linearly independent, then A is diagonizable.