Non-Homogeneous Cases

Practice Questions

Linear Algebra › Non-Homogeneous Cases

Page 1 of 2

10 of 20

$\begin{align*}&\text{Find }\begin{bmatrix}x\y\end{bmatrix}\&\text{for the system: }\begin{bmatrix}1&16\-10&-11\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}136\-2\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Find }\begin{bmatrix}x\y\end{bmatrix}\&\text{for the system: }\begin{bmatrix}12&18\-20&6\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}7\-10\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Find }\begin{bmatrix}x\y\end{bmatrix}\&\text{for the system: }\begin{bmatrix}4&18\-16&16\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}20\-29\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Solve the system of equations: }\begin{bmatrix}-5&-16\19&-3\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}-167\87\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Find }\begin{bmatrix}x\y\end{bmatrix}\&\text{for the system: }\begin{bmatrix}16&-11\-10&6\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}-78\131\end{bmatrix}\end{align*}$

Give the partial fractions decomposition of $\frac{4}{x^{3}+ 4x^{2}- 3x -12 }$ .

It is recommended that you use a calculator with matrix arithmetic capability for this question.

The graph of a quartic (degree four) polynomial passes through the following five points:

, , , ,

What is the cubic term of ?

Round to four decimal digits.

$\begin{align*}&\text{Find the values of }\begin{bmatrix}x\y\end{bmatrix}\&\text{for the function: }\begin{bmatrix}7&15\0&-18\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}-8\6\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Find }\begin{bmatrix}x\y\z\end{bmatrix}\&\text{for the system: }\begin{bmatrix}-3&-15&6\15&-9&14\-18&-5&-10\end{bmatrix}\begin{bmatrix}x\y\z\end{bmatrix}=\begin{bmatrix}-14\5\-8\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Find }\begin{bmatrix}x\y\end{bmatrix}\&\text{for the system: }\begin{bmatrix}12&-6\-2&-5\end{bmatrix}\begin{bmatrix}x\y\end{bmatrix}=\begin{bmatrix}7\3\end{bmatrix}\end{align*}$

Page 1 of 2

Return to subject