Review attached MATLAB Basics Dorfpdf file and do problems A

Review attached \"MATLAB Basics (Dorf).pdf\" file and do problems A1, A2 and A3 below of: Consider the two matrices: A = [4 2 pi 6j 10 + Squareroot 2 j] B = [6j -13 pi pi 16] Using MATLAB, compute the following: (a) A + B (b) AB (c) A^2 (d) A\' (Same as A^H i.e. complex conjugate transpose. For transpose use A\'.) (e) B^-1 (f) B\' A\' (g) A^2 + B^2 - AB Consider the following set of linear algebraic equations: 5.x + 6y + 10z = 4, -3x + 14z = 10, -7y + 21z = 0. Determine the values of x, y, and z so that the set of algebraic equations is satisfied.

Solution

A.2

5x + 6y + 10z = 4

3x + 14z = 10

-7y + 21z = 0

In this problem we do not have the system of linear equations in the form AX = B.
use equationsToMatrix to convert the equations into the form AX=B.

Declare the system of equations.

syms x y z
eqn1 = 5*x + 6*y + 10*z == 4;
eqn2 = -3*x + 0*y + 14*z == 10;
eqn3 = -7*x + 0*y + 21*z == 0;

Use equationsToMatrix to convert the equations into the form AX = B.
The second input to equationsToMatrix specifies the independent variables in the equations.

[A,B] = equationsToMatrix([eqn1, eqn2, eqn3], [x, y, z])

A =
[ 5, 6, 10]
[ -3, 0, 14]
[ -7,0, 21]

B =
   4
   10
   0

Use linsolve to solve AX = B for the vector of unknowns X.

X = linsolve(A,B)

X =
-16/11
   93/77
   31/77

From X, x = -16/17, y = 93/77 and z = 31/77