% q1
a = [1 3 2; 2 3 1; 1 2 -1]
determinant=det (a)
% ans = 6

% q2
syms x y z
[x,y,z] = solve(x + 3*y + 2*z == 4, 2*x + 3*y + z == 2, x + 2*y - z == -4)
% ans = x = 1, y = -1, z = 3

% q3
A = [2 1 2; 4 6 1; 1 -1 1]
B = [1 2 4; 3 2 1; 0 1 5]

% 1
A*B
% ans = [5 8 19; 22 21 27; -2 1 8]

% 2
A-B
% ans = [1 -1 -2; 1 4 0; 1 -2 -4]

% 3
A+B
% ans = [3 3 6; 7 8 2; 1 0 6]

% 4
B'
% ans = [1 3 0; 2 2 1; 1 0 6]

% q4
a = [1 1 3]
b = [4 2 -3]
cross(a, b)
% ans = -9 15 -2

% q5
e = [7 6 5]
f = [3 -2 -4]
dot(e, f)
% ans = -11

% q6
length(e), length(f)
% ans = e = 3, f = 3

% q7
a = [1 1 3]
sqrt(a)
% ans = 1.0000    1.0000    1.7321

% q8

syms x

% 1
diff(3*x^4)
% ans = 12*x^3

% 2
diff(sin(5*x) + cos(6*x))
% ans = 5*cos(5*x) - 6*sin(6*x)

% 3
diff(3*(2-x*4)^2)
% ans = 96*x - 48

% 4
diff((2*x)*(exp(2*x)))
% ans = 2*exp(2*x) + 4*x*exp(2*x)

% q9

% 1
syms x
solve((x+2)/2) + ((x-1)/3) == (((x*2)-2)/6)
% ans = x/3 - 7/3 == x/3 - 1/3

% 2
syms x
solve((x^2)*2-x-6==0)
% ans = -3/2, 2