2. (20 points) Consider the nx n square "almost tridiagonal” matrix T, (n> 5), which elements are given as follows. The

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2 20 Points Consider The Nx N Square Almost Tridiagonal Matrix T N 5 Which Elements Are Given As Follows The 1 (46.27 KiB) Viewed 20 times

2. (20 points) Consider the nx n square "almost tridiagonal” matrix T, (n> 5), which elements are given as follows. The nonzero elements of T are given by: • The Main diagonal of T where T(1,1) = 2 and T(i,i) = 5/2, Vi= 2. ...n • The first Upper diagonal of T, where: T(i,i+1) = 1, for i = 1,2,...n-1 • The first Lower diagonal of T, where: T(i,i-1) = 1, for i = 2, ...n . The (n - 2) Lower diagonal of T, where the 2 elements T(m - 1, 1) = Tn, 2) = Ta 1,11 4 (a) (3 points) Write T for n = 6 and show that the matrix T is strictly diagonally dominant for all n.