Question

Given the system of equations:

2 x + y + z = 2 − x + y − z = 3 x + 2 y + 3 z = − 10

Write 3 different MATLAB scripts/instructions to solve the above system of equations.

Your answer must indicate:

1. Solution 1: <statement(s)>
2. Solution 2: <statement(s)>
3. Solution 3: <statement(s)>

Answer 1

Solution 1:

• Define two matrices A and b of the form AX = b
• get X by doing A\b

A = [2 1 1; -1 1 -1; 1 2 3];

b = [2;3;-10];

X = A\b

A = [2 1 1; -1 1 -1; 1 2 3]; b [2;3;-10]; X = Alb X = 3x1 3 1 -5

solution 2:

• declare x y and z as symbols
• declare three symbolic equations e1, e2, e3 representing the given system of equations
• from this system of equations, get A and b matrices of AX = b using equationsToMatrix() function
• solve for X using linsolve()

syms x y z

e1 = 2*x + y + z == 2;

e2 = -x + y -z == 3;

e3 = x + 2*y + 3*z == -10;

[A,b] = equationsToMatrix([e1, e2, e3])

X = linsolve(A,b)

syms x y z el 2*x + y + z == 2; e2 = -x + y - Z == 3; e 3 = x + 2 y + 3* z == -10; [A,b] = equationsToMatrix ([el, e2, e3]) A = 1 1 2 - 1 1 - 1 1 2 2 3 b = 2 3 10 X = linsolve (A,b) 3 1

solution 3:

• using solve() to solve the system of equation e1, e2 and e3. It will return a struct with fields x, y and z. these fields contain the soltion for x, y and z respectively

syms x y z

e1 = 2*x + y + z == 2;

e2 = -x + y -z == 3;

e3 = x + 2*y + 3*z == -10;

X = solve([e1,e2,e3],[x, y, z]);

x = X.x

y = X.y

z = X.z

(D syms x y z 2*x + y + z == 2; e2 = -x + y - Z e 3 = x + 2 y + 3* z == -10; == 3 x solve (fel,e2, e3], [x, y, z]); X = X.X x = 3 y = X. y y = 1 z = X. z z = -5