%Sol2
%----- Q1 -----

A = [2 3; 4 5]
x = [1; -7]
b = [24; 5]
if A*x == b
    display("Ax equals b");
else display ("Ax is not equal to b");
end

%----- Q2 -----
A = eye(3)
v = [3:5]'
A*v
%A*v = v
v'*v
%dot product of v and v which is 50
%41833
% v*A creates problem because v is 3X1 where A is 3x3; so multiplication is not possible


%----- Q3 -----
A = ones(4)
v = ones(4,1)
disp("A*v is: ")
A*v
B = eye(4) + ones(4)
w = zeros(4,1) + 2*ones(4,1)
disp("B*w =")
B*w


%----- Q4 -----
P = pascal(4)
inv(P)

%----- Q5 -----
L = abs(pascal(4,1))
if P == L*L'
    disp("P equals LL'")
else disp("P is not equal to LL'")
end