Reference no: EM132405533

Assignment on Linear Systems

1. Consider the system

D_x = b - αc                 (i)

where D ∈ R^nxn, b ∈ Rⁿ, c ∈ Rⁿ and ξ₁ with x = (ξ_i) ∈ Rⁿ are given. Show how α ∈ R and the remaining of x may be computed so that (1) is satisfied. Your approach should use matrix and vector operations as much as possible. Implement your approach in Matlab using a script function that uses vectorization. Hint: Vectorization is for example the use of z = x*' + y instead of

for i = 1:n
z(i) = x(i) + y(i);
end

2. Write a Matlab script program that computes efficiently

ζ = d^T B^T E^-1Bd

when d ∈ Rⁿ, E ∈ R^nxn, B ∈ R^nxn are given.

Generate data using the given Matlab script program InpLinSys.m and run your script functions on these data.

Attachment:- Linear Systems.rar