Question

4. The matrix A of order n x n is given by
A = I - X(X'X)-1 X' where I is an identity
matrix and X' is the transpose of X. What can
you conclude about the order of X?

Answer 1

Step-by-step explanation:

• As far as linear algebra is concerned, the two most important operations with vectors are vector addition [adding two (or more) vectors] and scalar multiplication (multiplying a vectro by a scalar). Analogous operations are defined for matrices. Matrix addition. If A and B are matrices of the same size, then they can be added. (This is similar to the restriction on adding vectors, namely, only vectors from the same space R n can be added; you cannot add a 2‐vector to a 3‐vector, for example.) If A = [aij] and B = [bij] are both m x n matrices, then their sum, C = A + B, is also an m x n matrix, and its entries are given by the formula