Final answer:
The question involves solving the least squares problem with a given orthonormal matrix A and vector b. However, the provided matrix and vector information appears incomplete, and unrelated equations are included, which are not useful in solving the least squares problem without further context or correct data.
Step-by-step explanation:
The student's question pertains to solving the least squares problem for a given matrix A and vector b. The matrix A is described as having orthonormal columns, which means each column is at a 90-degree angle (orthogonal) to the others, and each vector is of unit length (normal). To solve the least squares problem Ax = b, one typically uses the formula ATAx = ATb, where AT is the transpose of A. Since the columns of A are orthonormal, ATA will equate to the identity matrix, making the calculation simpler.
In this question, however, the matrix and vector provided do not seem complete, and the text includes unrelated equations about vectors and scalar products, which are not directly applicable to solving the least squares problem mentioned. Therefore, without additional context or correct inputs, a valid solution cannot be provided. The student may need to recheck the provided matrix A and vector b for any missing elements or typos.