Let Rk be a k k upper triangular matrix and suppose that RkUk = UkDk where Uk is an upper triangular matrix with 1s on the diagonal and Dk is a diagonal matrix. Let Rk+1 be an upper triangular matrix of the form Rk bk 0T k where k is not an eigenvalue of Rk . Determine (k + 1) (k + 1) matrices Uk+1 and Dk+1 of the form Uk+1 = Uk xk 0T 1 , Dk+1 = Dk 0 0T such that Rk+1Uk+1 = Uk+1Dk+1 1

M344 Section 7.4 Notes- Basic Theory of Systems of First Order Linear Equations 1-31-17 ′ 1= 11( 1+ 12( 2+ ⋯+ 1( + 1) Consider system { ⋮ ; closely parallels single linear = ( + ( + ⋯+ ( + ()...