Answer :
Final answer:
The question involves computing the orthogonal projection of vector b onto the column space of matrix or vector a using the projection operator formula where PAB is the projection of B onto A, and involves dot products and scaling.
Explanation:
The student's question is related to finding the orthogonal projection of a vector b onto the column space of another vector or matrix a. In linear algebra, this is accomplished using the formula for the projection operator given a column vector A and a column vector B, the orthogonal projection of B onto A is given by the expression PAB = (A⋅B)/(A⋅A) × A, where ⋅ denotes the dot product. Considering the column space of a matrix a essentially involves computing the projection onto each column vector of a and summing the results, assuming the columns of a are orthogonal.
If we have specific vectors A and B, and A represents the column space of matrix a, we can apply this formula to get the coordinates [c1, c2, c3] for the projection of B onto A. The detailed steps would require calculating the dot products and the scaling according to the given formula.
