Proof please

Prove that ||x^(k) - x|| <= (||T||^k)(||x^(0) - x||) and ||x^(k) - x|| <= (||T||^k/(1-||T||))(||x^(1)-x^(0)||), where T is an n x n matrix with ||T|| < 1 and x^(k)=Tx^(k-1)+c, k=1,2,..., with x^(0) arbitrary, c belonging to R^n, and x=Tx+c

test

only problems #3 &4-a,(without using any software).

Math - Knots

Only solve 4 part A, and 5 using MATLAB Codes.

newtons method

Please show that when n=1, Newtons method given by: x^k=x^(k-1)-(J(x^(k-1))^-1)(F(x^(k-1)) for k>=1 reduces to the familiar Newton's method given by: P_n=P_n-1 - f(p_n-1)/f'(P_n-1) for n>=1 Note: ^-1 is inverse J is the jacobian matrix The top equation is called newton's method for non linear systems. x is a vector. F(x_1,...,x_n)=(f_1(x_1,...,x_n),f_2(x_1,...,x_n),...,f_n(x_1,...,x_n))

MATLAB \ Least Squares -- solving overdeterminded or inexactly specified of equations in approximation

The solution can ONLY be accepted in Matlab. Matlab 7.0 is preferable. The problem is in the attachment file. Thank you.