Given a matrix
[ A=left[egin{array}{cccc} -1 & 2 & -3 & 4 \ 2 & -5 & 6 & -7 \ -3 & 6 & 8 & -9 \ 4 & -7 & -9 & 10 end{array}
ight] ]
Starting with a ( x_{0}=(1,0,0,0)^{T} ), use Matlab and the power method with Euclidean scaling (meaning making ( left|x^{(n)}
ight|=1 ) ) to find the dominant eigenvalue and a unit dominant eigenvector of A. List down the successive approximations ( lambda^{(n)} ) and ( x^{(n)} ) of the dominant eigenvalue and dominant unit eigenvector, displaying 4 decimal places for ( lambda^{(n)} ) and ( x^{(n)} ) with ( n=1,2, cdots, 15 ).