Linear Equations

Practice Questions

Linear Algebra › Linear Equations

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$\begin{align*}&\text{Convert }A=\begin{bmatrix}4&-9&-10\-11&-13&-5\\end{bmatrix}\&\text{to its reduced echelon form.}\end{align*}$

$\begin{align*}&\text{Is there a unique solution for the equation }\&\begin{bmatrix}-20&12\7&16\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}-171\149\end{bmatrix}?\end{align*}$

$\begin{align*}&\text{Determine whether or not the equation }\&\begin{bmatrix}6&-8\3&12\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}-188\-101\end{bmatrix}\&\text{has a unique solution.}\end{align*}$

$\begin{align*}&\text{Is there a unique solution for the equation }\&\begin{bmatrix}0&-8&2\-5&3&2\20&12&-14\end{bmatrix}\begin{bmatrix}x\y\z\end{bmatrix}=\begin{bmatrix}-163\36\22\end{bmatrix}?\end{align*}$

$\begin{align*}&\text{Is there a unique solution for the equation }\&\begin{bmatrix}13&13&-2\12&12&12\-16&-16&-11\end{bmatrix}\begin{bmatrix}x\y\z\end{bmatrix}=\begin{bmatrix}28\125\107\end{bmatrix}?\end{align*}$

$\begin{align*}&\text{Determine whether or not the equation }\&\begin{bmatrix}16&-11\-17&6\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}-8\153\end{bmatrix}\&\text{has a unique solution.}\end{align*}$

$\begin{align*}&\text{Determine whether or not the equation }\&\begin{bmatrix}2&-5&-12\8&7&1\-10&-2&11\end{bmatrix}\begin{bmatrix}x\y\z\end{bmatrix}=\begin{bmatrix}-71\-38\-50\end{bmatrix}\&\text{has a unique solution.}\end{align*}$

$\begin{align*}&\text{Decide if there is a unique solution for the equation: }\&\begin{bmatrix}19&-12\9&18\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}-126\-163\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Find nonzero solutions for }\begin{bmatrix}x\y\z\end{bmatrix}\&\text{for the system: }\begin{bmatrix}-19&-13&18\18&-2&13\\end{bmatrix}\begin{bmatrix}x\y\z\end{bmatrix}=\begin{bmatrix}0\0\\end{bmatrix}\end{align*}$

Find the inverse using row operations

$\begin{bmatrix} 2 &7 &1 \-1 &5 &3 \ 2& 2& -1\end{bmatrix}$

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