Chapter 7, Problem 12SE

(a)

To determine

To verify: that “For each y in ${ℝ}^m$, $A{A}^{+}\text{y}$ is the orthogonal projection of y onto Col A”.

(b)

To determine

To verify: that “For each x in ${ℝ}^n$, $A^{+}A\text{x}$ is the orthogonal projection of x onto RowA”.

Part (c):

To determine

To verify: that “ $A{A}^{+}A=A\text{and }{A}^{+}A{A}^{+}=A^{+}$”.