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2. Assume you want solve AX = b, where the column coefficient matrix are independent as shown below: \begin{equation} A = \begin{bmatrix} 1 & 1 & 1 \ -1 & 0 & 1 \ 1 & 1 & 2 \end{bmatrix} \end{equation} (a) Use Gram-Schmidt method to find the orthogonal column vectors of A. (b) Use the orthogonal vectors to solve AX = b, where b = [1,2,3]' (c) Use Gram-Schmidt method to find the orthonormal vector Q and upper triangular matrix R such that A = QR. (d) Write a Matlab function to decompose a matrix A in to QR. (e) Use the power method to find the largest eigen value and its corresponding eigen vector. (f) Write Matlab function to find the largest eigen value and its corresponding eigen vector for any matrix A.

          2. Assume you want solve AX = b, where the column coefficient matrix are independent as shown below:
\begin{equation*}
A = \begin{bmatrix} 1 & 1 & 1 \ -1 & 0 & 1 \ 1 & 1 & 2 \end{bmatrix}
\end{equation*}
(a) Use Gram-Schmidt method to find the orthogonal column vectors of A.
(b) Use the orthogonal vectors to solve AX = b, where b = [1,2,3]'
(c) Use Gram-Schmidt method to find the orthonormal vector Q and upper triangular matrix R such that A = QR.
(d) Write a Matlab function to decompose a matrix A in to QR.
(e) Use the power method to find the largest eigen value and its corresponding eigen vector.
(f) Write Matlab function to find the largest eigen value and its corresponding eigen vector for any matrix A.

2. Assume you want solve AX = b, where the column coefficient matrix are independent as shown below:

A =
< b m a t r i x >

(a) Use Gram-Schmidt method to find the orthogonal column vectors of A.
(b) Use the orthogonal vectors to solve AX = b, where b = [1,2,3]'
(c) Use Gram-Schmidt method to find the orthonormal vector Q and upper triangular matrix R such that A = QR.
(d) Write a Matlab function to decompose a matrix A in to QR.
(e) Use the power method to find the largest eigen value and its corresponding eigen vector.
(f) Write Matlab function to find the largest eigen value and its corresponding eigen vector for any matrix A.

Added by Elizabeth B.

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