Question: Let Rk be a k Ã k upper triangular matrix and suppose that RkUk = UkDk where Uk is an upper triangular matrix with l's

Let Rk be a k Ã— k upper triangular matrix and suppose that
RkUk = UkDk
where Uk is an upper triangular matrix with l's on the diagonal and Dk is a diagonal matrix. Let Rk+1 be an upper triangular matrix of the form

where Î²k is not an eigenvalue of Rk- Determine (k + 1) Ã— (k + 1) matrices Uk+1 and Dk+1 of the form

Such that
Rk+1Uk+1 = Uk+1Dk+1

Dk 0 or

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