Chapter 5 - Inner Product Spaces - 5.4 Least Squares Approximation - True-False Review - Page 375: c

True

The least squares solution: $x_0=(A^TA)^{-1}A^Tb$ If A is an n×n invertible matrix then $A^T(A^T)^{-1}=(A^T)^{-1}A^T=I$ Apply to the least squares solution we have: $x_0=(A^TA)^{-1}A^Tb$ $\rightarrow x_0=A^{-1}(A^T)^{-1}A^Tb$ $\rightarrow x_0=A^{-1}b$ Thus, the statement is true.