Find a least-squares solution of the inconsistent system Ax = b.
-$$\mathrm { A } = \left[ \begin{array} { l l }
1 & 2 \
3 & 4 \
5 & 9
\end{array} \right] , \mathrm { b } = \left[ \begin{array} { l }
1 \
5 \
1
\end{array} \right]$$
A)
$$\left[ \begin{array} { c }
\frac { 73 } { 1754 } \
- \frac { 77 } { 3508 }
\end{array} \right]$$
B)
$$\left[ \begin{array} { c }
\frac { 121 } { 42 } \
- \frac { 51 } { 28 }
\end{array} \right]$$

C)
$\left[\begin{array}{l}
-\frac{2}{21} \
-\frac{11}{6}
\end{array}\right]$

D)

$\left[\begin{array}{c}
\frac{146}{27} \
-\frac{77}{27}
\end{array}\right]$

Question

Find a least-squares solution of the inconsistent system Ax = b.
-$$\mathrm { A } = \left[ \begin{array} { l l } 
1 & 2 \
3 & 4 \
5 & 9
\end{array} \right] , \mathrm { b } = \left[ \begin{array} { l } 
1 \
5 \
1
\end{array} \right]$$
A)
$$\left[ \begin{array} { c } 
\frac { 73 } { 1754 } \
- \frac { 77 } { 3508 }
\end{array} \right]$$
B)
$$\left[ \begin{array} { c } 
\frac { 121 } { 42 } \
- \frac { 51 } { 28 }
\end{array} \right]$$

C)
$\left[\begin{array}{l}
-\frac{2}{21} \
-\frac{11}{6}
\end{array}\right]$

D)

$\left[\begin{array}{c}
\frac{146}{27} \
-\frac{77}{27}
\end{array}\right]$

Quizplus · Accepted Answer

The least-squares solution is found by solving the normal equations $A^TAx = A^Tb$. Solving these equations for the given matrices results in the solution provided in option D.

Find a Least-Squares Solution of the Inconsistent System Ax =