16.1 Three variables x, y, and z are required to satisfy the equations
Is there a solution in the normal sense, not a least-squares solution? If so, is it unique, or are there infinitely many solutions?
16.2 If A is an invertible matrix and assuming exact arithmetic, are the solutions using Gaussian elimination and least squares identical? Prove your assertion.
16.3 If A is an m × n matrix, m ≥ n, and b is an m × 1 vector, show that if ATb = 0, b is orthogonal to the range of A.
16.4 If A is an m × n full-rank matrix, m ≥ n, show that
where σ1 and σn are the largest ...