10. Systems of Differential Equations

Matrix Form — Quiz

Test your understanding of matrix form with 5 practice questions.

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Practice Questions

Question 1

Which matrix equation represents the system $x'=2x-y$ and $y'=3x+4y$?

Question 2

In the matrix system $\mathbf{X}'=A\mathbf{X}$ for $u'=5u+2v$ and $v'=-u+3v$, what is $A$?

Question 3

If $\mathbf{X}=\begin{pmatrix}x\y\z\end{pmatrix}$ in $\mathbf{X}'=A\mathbf{X}$, what size must $A$ be?

Question 4

If $\mathbf{X}'=\begin{pmatrix}1&-4\\2&0\end{pmatrix}\mathbf{X}$ and $\mathbf{X}=\begin{pmatrix}x\y\end{pmatrix}$, what is the second differential equation?

Question 5

Which vector correctly represents the dependent variables for a system with variables $p$, $q$, and $r$?