Least Squares

Practice Questions

Linear Algebra › Least Squares

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$\begin{align*}&\text{Approximate }\begin{bmatrix}x\y\end{bmatrix}\&\text{for the system: }\begin{bmatrix}-12&9\13&14\-5&-16\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}-100\-5\14\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Approximate the values of }\begin{bmatrix}x\y\end{bmatrix}\&\text{for the function: }\begin{bmatrix}20&-19\-9&-18\14&-10\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}-8\11\37\end{bmatrix}\end{align*}$

Let $y=(1 \ 2 \ 3 \ 4 \ 5 \10 )$ , and $x=(0 \ 1 \ 2 \3 \4 \5)$ , find the least squares solution for a linear line.

$\begin{align*}&\text{Approximate the values of }\begin{bmatrix}x\y\end{bmatrix}\&\text{for the function: }\begin{bmatrix}15&15\-7&-12\-3&9\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}-120\-4\-180\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Using the method of least-squares, approximate x and y values for: }\&\begin{bmatrix}15&-4\19&-15\-2&19\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}-195\-163\15\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Approximate }\begin{bmatrix}x\y\end{bmatrix}\&\text{for the system: }\begin{bmatrix}11&4\-8&0\8&20\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}-42\-66\-36\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Using the method of least-squares, approximate x and y values for: }\&\begin{bmatrix}14&-9\-10&-4\-8&-6\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}-12\-198\-179\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Approximate the values of }\begin{bmatrix}x\y\end{bmatrix}\&\text{for the function: }\begin{bmatrix}-13&12\-12&1\-2&19\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}-103\-178\-16\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Using the method of least-squares, approximate x and y values for: }\&\begin{bmatrix}1&-17\-6&1\1&-13\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}188\149\19\end{bmatrix}\end{align*}$