7.4 Let A be a symmetric positive definite n × n matrix and let b be an n-vector.

Consider the minimization problem minimize xTAx such that bTx = 1, over x ∈ ℝn. Show that the solution is given by x = A−1b∕(bTA−1b).

Hint: Using a Lagrange multiplier ????, minimize the unconstrained objective function xTAx + 2????(1 − bTx) over x ∈ ℝn to get x = ????A−1b, and show that the constraint is satisfied if ???? = 1∕(bTA−1b).