Homogeneous Cases

Practice Questions

Linear Algebra › Homogeneous Cases

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

$\begin{align*}&\text{Find the nontrivial solutions for the system of equations: }\&\begin{bmatrix}-10&2&-11\-20&11&-20\\end{bmatrix}\begin{bmatrix}x\y\z\end{bmatrix}=\begin{bmatrix}0\0\\end{bmatrix}\end{align*}$

Consider the system of linear equations:

Which of the following gives its complete solution set (in parametric form, if applicable) or its only solution?

$\begin{align*}&\text{Find nonzero solutions for }\begin{bmatrix}x\y\z\end{bmatrix}\&\text{for the system: }\begin{bmatrix}-5&-1&13\-8&13&3\\end{bmatrix}\begin{bmatrix}x\y\z\end{bmatrix}=\begin{bmatrix}0\0\\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Find nonzero solutions for }\begin{bmatrix}x\y\z\end{bmatrix}\&\text{for the system: }\begin{bmatrix}-7&-2&-11\-19&6&-14\\end{bmatrix}\begin{bmatrix}x\y\z\end{bmatrix}=\begin{bmatrix}0\0\\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Find the nontrivial solutions for the system of equations: }\&\begin{bmatrix}8&-13&12\1&2&-12\\end{bmatrix}\begin{bmatrix}x\y\z\end{bmatrix}=\begin{bmatrix}0\0\\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Find the nontrivial solutions for the system of equations: }\&\begin{bmatrix}-6&-16&2\-3&1&16\\end{bmatrix}\begin{bmatrix}x\y\z\end{bmatrix}=\begin{bmatrix}0\0\\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Find the nontrivial solutions for the system of equations: }\&\begin{bmatrix}-2&13&12\-9&-18&-18\\end{bmatrix}\begin{bmatrix}x\y\z\end{bmatrix}=\begin{bmatrix}0\0\\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Find nontrivial solutions of }\begin{bmatrix}x\y\z\end{bmatrix}\&\text{for the function: }\begin{bmatrix}11&16&-15\12&-13&-19\\end{bmatrix}\begin{bmatrix}x\y\z\end{bmatrix}=\begin{bmatrix}0\0\\end{bmatrix}\end{align*}$

Consider the system of linear equations:

Which of the following expresses the solution set in parametric form?

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