Find a 3 x 3 matrix • The vectors V₁ = satisfying the following properties: • A has two eigenvalues: A₁ = -3 and X₂ 3] 3 -3 and V₂ H -2 are eigenvectors of A corresponding to X₁. • The vector V3 = How to enter matrices. = then you should do it as follows: A = = -3. Enter the matrix A: a11 a12 a13 a21 a22 a23 a31 a32 a33 2 -3 is an eigenvector of A corresponding to A2. Martices should be entered row by row, enclosing each row in square brackets. There must be additional square brackets at the beginning and at the end of the whole matrix. For example, if you want to enter the matrix 2 [8 MIN HIN Do not forget about commas between matrix entries and between rows. A 2 [[2, -3/2, 4], [0, 1/2, 2]]

Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are -2 and 7. 3 - 4 - 2 -4 3 - 2 -2 -2 6 Enter the matrices P and D below. (Use a comma to separate matrices as needed. Type exact answers, using radicals as needed. Do not label the matrices.)

Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are - 10, 2, and - 2. - 4 - 4 - 2 A = - 4 -2 - 4 2 -4 - 4 Enter the matrices P and D below. (Use a comma to separate answers as needed. Type exact answers, using radicals as needed. Do not label the matrices.)

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