Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Digital systems, linear algebra, introduction to formal proof resit / 4 / a

The update must place the sum of the two current entries in the first coordinate and retain the old first coordinate in the second. Thus choose the matrixBy matrix multiplication, $A(L_n,L_{n-1}{)}^T=(L_n+L_{n-1},L_n{)}^T=(L_{n+1},L_n{)}^T$ for every $n\ge 1$, using the given recurrence relation. This is the companion-matrix representation of the Lucas numbers.