Let A be a banded positive definite matrix with bandwidth p, and let b be a vector with all elements zero excepting just one nonzero element. How much work does it take to compute bT A−1 b? Compute...

Let A be a banded positive definite matrix with bandwidth p, and let b be a vector with all elements zero excepting just one nonzero element. How much work does it take to compute bT A−1 b?

Compute the 5 × 5 matrix V whose elements are Vij = xi−1 , xj−1  =  1 −1 xi+j−2 dx. Have you seen this matrix before?