[Solved] MATH307 Individual Homework14

Instructions: Read textbook pages 67 to 68 before working on the homework problems. Show all steps to get full credits.

1. Let A F^mn, with F = R or C, prove that range(A) is orthogonal to null(A), i.e., any arbitrary vector in range(A) is orthogonal to an arbitrary vector in null(A).
2. Use Gram-Schmidt method to find a QR factorization of the matrix

1 2 1

A = 3 1 1 .

1 1 2

3. Consider a matrix A F^mn with m n and all columns being orthogonal but not of unit length, what should its reduced QR decomposition look like?