When solving a system of equations A x b Matrix A is illcon

When solving a system of equations A x = b. Matrix A is ill-conditioned. Do we get the same values of x if b is represented using single-precision floating-point format or double-precision floating-point format for any values of b? please explain why?

Solution

When solving a system of equations A x = b. Matrix A is ill-conditioned. Do we get the same values of x if b is represented using single-precision floating-point format or double-precision floating-point format for any values of b? please explain why?

Ax=b.
Matrix A is ill-conditioned.
X if b represent using single- precision floating-point format or double-precision floating-point format
x=single(25.783);
xAttrib = whos(\'x\');
zAttrib.bytes
for a number x of type double,eps(single(x)) gives you an upper bound for the amount x is rounded when you convert it form double to single. for example, when you convert the double-precision number 3.14 to single, it is rounded by

double(single(3.14)-3.14)
ans=
1.0490e-07
The amount that 3.14 is rounded is less than
eps(single(3.14))
ans=
single
2.3842e-07