SOLVE EXERCISE 16.1 and 16.2 please. show code and ideally use matlab.

or, componentwise, as ard solve the system of equations Ax = b using the three alternative methods i) x = A-lb, (the inverse A-1 may be com- puted in Matlab using inv (A).) ii) x = A \ b, iii) x'Ar-b' leading to2T = b, / Awhich When A is non-singular and square (n meaning that the number of independent equa tions is equal to the number of unknowns, the system has a unique solution given by makes use of the "slash" or "right divi- uired solution is then the transpose of the rou) vector T n), sion" operator "". The Exercise 16.2 Use the backslash operator to solve the complex system of equations for which x = A-lb where A-1 is the inverse of A. Thus, the solu tion vector x can, in principle, be calculated by taking the inverse of the coefficient matrix A and multiplying it on the right with the right hand-side vector b This approach based on the matrix inverse, thoughtrix interston com mana formally correct, is at best inefficient for prac meth tical applications (where the number of equa- What kind of matrices tions may be extremely large) but may also give applicable to? rise to large numerical errors unless appropr Obviously problems may occthe inverted ate techniques are used. These issues are dis matriz is nearly sin cussed in most courses and texts on numerical that c methods. Various stable and efficient solution the matrix is nearly singular techniques have been developed for solving lin the topics referred ear equations and the most appropriate in any situation will depend on the properties of the 16.1 Omn coefficient matrix A. For instance, on whethe 2+2i-1 0 1+i 16.3 Find information on the ma- o raing help command uggest a command n indication on whether Hint: see An overdeterm rem of linear equations is nknowns if it has a particular structure (sparse or fu Lmore equacious Matlab is equipped with many of these special (n), le techniques in its routine library and many are than columns (m invoked automatically The standard Matlab routine for solving sys- elling when the paramo tems of linear equations is invoked by calling terminedb the matrix left-division routine, has more rows verdetermined sys- ar in mathematical mod- e- o experimental data. For- looks the same as for square tems freque mally the sy systems but the coen lar and OSSIDIe to compute an n cases a solution can be found of the residual where "is the matrix left-division operator Verse known as "backslash" (see help backslash). by requiring that ue Exercise 16.1 Enter the symmetric coefficient matriz and right-hand-side vector b given by vector r, d 2 -1 0 A=11-21 0 -1 2 be minimized. The simnles use the Euclidean length (or norm-see Section 12.1) t frequently the magnituae UL quire