Answer Happy

2.6 LS Solution by Backslash Operator and QR Decomposition The backslash ("A\b') operator and the matrix left division ('mldivide (A,b)") function turn out to be the most efficient means for solv- ing a system of linear equations as Eq. (P2.3.1). They are also capable of dealing with the under/over-determined cases. Let's see how they handle the under/over-determined cases. (a) For an underdetermined system of linear equations A₁x=b₁. - [14] (P2.6.1) X3 find the minimum-norm solution (2.1.7) and the solutions that can be obtained by typing the following statements in the MATLAB command window: >>A1 [1 2 3; 4 5 6]; b1 [14 321¹; >>x_mn = A1¹* (A1*A1')-1 b1, x pi= pinv (A1)*b1, x_bs = A1\b1 Are the three solutions the same? (b) For another underdetermined system of linear equations A₂x = b₂. [²8-4 (P2.6.2) find the solutions by using Eq. (2.1.7), the commands pinv(), and back- slash (\). If you are not pleased with the result obtained from Eq. (2.1.7). you can remove one of the two rows from the coefficient matrix A₂ and try again. Identify the minimum solution(s). Are the equations redundant or inconsistent? SYSTEM OF LINEAR EQUATIONS Table P2.6.1 Comparison of Several Methods for Computing the LS Solution QR LS: Eq. (2.1.10) pinv(A)"b A\b ||Ax-b|| # of flops 2.8788e-016 25 2.8788e-016 196 89 92 110