Question

(1 point) For each of the following, factor the matrix A into a product $QDQT$ where Q is orthogonal and D is diagonal. (a) A = \begin{bmatrix} 7 & 1 & 1 \\ 1 & 5 & 3 \\ 1 & 3 & 5 \end{bmatrix} Q = \begin{bmatrix} 0 & & -2 & & 1 \\ & & 1 & & 1 \\ 1 & & 1 & & 1 \end{bmatrix} D = \begin{bmatrix} 2 & & 0 & & 0 \\ & & 0 & 6 & 0 \\ 0 & & 0 & & 9 \end{bmatrix} (b) A = \begin{bmatrix} 4 & -2 & 2 \\ -2 & 3 & -3 \\ 2 & -3 & 3 \end{bmatrix} Q = \begin{bmatrix} & & \\ & & \\ & & \end{bmatrix} D = \begin{bmatrix} 0 & & 0 & & 0 \\ & & 0 & 2 & 0 \\ 0 & & 0 & & 8 \end{bmatrix} LS: Given a symmetric matrix A, I can orthogonally diagonalize A.

          (1 point) For each of the following, factor the matrix A into a product $QDQT$ where Q is orthogonal and D is diagonal.
(a) A = \begin{bmatrix} 7 & 1 & 1 \\ 1 & 5 & 3 \\ 1 & 3 & 5 \end{bmatrix}
Q = \begin{bmatrix} 0 &  & -2 &  & 1 \\  &  & 1 &  & 1 \\ 1 &  & 1 &  & 1 \end{bmatrix}
D = \begin{bmatrix} 2 &  & 0 &  & 0 \\  &  & 0 & 6 & 0 \\ 0 &  & 0 &  & 9 \end{bmatrix}
(b) A = \begin{bmatrix} 4 & -2 & 2 \\ -2 & 3 & -3 \\ 2 & -3 & 3 \end{bmatrix}
Q = \begin{bmatrix}  &  &  \\  &  &  \\  &  &  \end{bmatrix}
D = \begin{bmatrix} 0 &  & 0 &  & 0 \\  &  & 0 & 2 & 0 \\ 0 &  & 0 &  & 8 \end{bmatrix}
LS: Given a symmetric matrix A, I can orthogonally diagonalize A.

(1 point) For each of the following, factor the matrix A into a product QDQT where Q is orthogonal and D is diagonal.
(a) A =
< b m a t r i x >

Q =
< b m a t r i x >

D =
< b m a t r i x >

(b) A =
< b m a t r i x >

Q =
< b m a t r i x >

D =
< b m a t r i x >

LS: Given a symmetric matrix A, I can orthogonally diagonalize A.

Added by David W.

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