Linear Algebra - Criteria for Uniqueness and Consistency

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

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

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

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

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

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

$\begin{align*}&\text{Decide if there is a unique solution for the equation: }\&\begin{bmatrix}-6&-7&-19\-8&19&-14\0&5&2\end{bmatrix}\begin{bmatrix}x\y\z\end{bmatrix}=\begin{bmatrix}-21\-36\-149\end{bmatrix}\end{align*}$

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

$\begin{align*}&\text{Decide if there is a unique solution for the equation: }\&\begin{bmatrix}1&11&14\-1&10&-12\11&-5&16\end{bmatrix}\begin{bmatrix}x\y\z\end{bmatrix}=\begin{bmatrix}59\4\-32\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Decide if there is a unique solution for the equation: }\&\begin{bmatrix}3&-14&-20\5&0&-3\-6&8&14\end{bmatrix}\begin{bmatrix}x\y\z\end{bmatrix}=\begin{bmatrix}125\155\-70\end{bmatrix}\end{align*}$

Criteria for Uniqueness and Consistency

Practice Questions