Question: Consider the matrix Find the Eigenvalues of the matrix A. Find two (linearly independent) eigenvectors for this matrix. Show that the two eigenvectors are

Consider the matrix

A= (2 2 -1

Find the Eigenvalues of the matrix A.

Find two (linearly independent) eigenvectors for this matrix.

Show that the two eigenvectors are perpendicular (by showing that their Inner product. r+ r = 0).

Find a similarity transformation, C, that will diagonally the matrix A (form the matrix C by normalizing the two eigenvectors and then using one of the normalized eigenvectors as the first column and the second normalized eigenvector as the second column).

Show that the matrix C is Unitary.

A= (2 2 -1

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Finding the eigenvalues of A To find the eigenvalues of A we solve the characteristic equation detA I 0 This gives us the quadratic equation 2 2 1 0 T... View full answer

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