Let be a known value, such as ones(n,1) and compute b = Ax. Theoretically, should be the known solution However, due to the nature of floating point computation the relative error / is not...

Let

be a known value, such as ones(n,1) and compute b = Ax. Theoretically,


should be the known solution

However, due to the nature of floating point computation the relative error
/
is not expected to be

but it should be small if

is not ill-conditioned. The idea for this problem is to observe ill-conditioning using the matrix
gallery(’lotkin’, n). Perform the steps presented in the following algorithm and comment on the results. The notation

in a print statement indicates the value to print. For instance,

print

The condition number of A is

condition number with 8 significant digits