Answer the following Questions :
Suppose that multiplying two general n by n matrices takes 3 seconds on a given computer, if n = 1000.
Estimate how much time it will take to compute the LU-decomposition of such a matrix.
Suppose that solving a general system of linear equations of dimension 1000 takes 10 seconds on a given computer.
Estimate how much time it will take to solve a tridiagonal linear system of dimension 106 on that computer.
How many divisions are needed for LU-decomposition of an n by n tridiagonal matrix (not counting multiplications and additions)?
How many divisions are needed for LU-decomposition of an n by n general matrix (not counting multiplications and additions)?