In MATLAB, create the following 20 x 10 matrix: A 1 = ( 101-19 110x10 10-8110x10...

 

 

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In MATLAB, create the following 20 x 10 matrix: A 1 = ( 101-19 110x10 10-8110x10 where 110x10 is a 10 x 10 matrix whose entries are all ones. This particular matrix has a very large condition number, since the columns of A are nearly linearly dependent. Consider the least-squares problem Ax = a. Solve this least-squares problem in MATLAB using the normal equation. That is, form the matrix ATA and solve ATAx = ATb. You may use MATLAB's backslash command to solve this system, or you may compute the inverse of ATA to solve for x directly. Are you able to get a solution? What (if any) warnings does MATLAB give you? b. Solve this least-squares problem in MATLAB by the QR equation. That is, obtain the re- duced QR factorization of A and solve Rx = QTb by MATLAB's backslash command or by computing the inverse of R. Note: Please use MATLAB's built-in QR factorization function as follows: [Q,R] = qr(A). Remember that MATLAB returns a full QR factorization. To get the reduced QR factoriza- tion, take only the first ten columns of Q and the first ten rows of R since A is a 2010 matrix. Rounded to the second decimal place, what is the solution x to this least-squares problem? Does this solution seem reasonable, i.e., does Axb for the least-squares solution x? In MATLAB, create the following 20 x 10 matrix: A 1 = ( 101-19 110x10 10-8110x10 where 110x10 is a 10 x 10 matrix whose entries are all ones. This particular matrix has a very large condition number, since the columns of A are nearly linearly dependent. Consider the least-squares problem Ax = a. Solve this least-squares problem in MATLAB using the normal equation. That is, form the matrix ATA and solve ATAx = ATb. You may use MATLAB's backslash command to solve this system, or you may compute the inverse of ATA to solve for x directly. Are you able to get a solution? What (if any) warnings does MATLAB give you? b. Solve this least-squares problem in MATLAB by the QR equation. That is, obtain the re- duced QR factorization of A and solve Rx = QTb by MATLAB's backslash command or by computing the inverse of R. Note: Please use MATLAB's built-in QR factorization function as follows: [Q,R] = qr(A). Remember that MATLAB returns a full QR factorization. To get the reduced QR factoriza- tion, take only the first ten columns of Q and the first ten rows of R since A is a 2010 matrix. Rounded to the second decimal place, what is the solution x to this least-squares problem? Does this solution seem reasonable, i.e., does Axb for the least-squares solution x?