3. Matrix Methods for Systems

Solving Via Inverse When Appropriate — Quiz

Test your understanding of solving via inverse when appropriate with 5 practice questions.

Practice Questions

Question 1

What condition must the coefficient matrix $A$ satisfy so that a system $A\mathbf{x}=\mathbf{b}$ can be solved using $\mathbf{x}=A^{-1}\mathbf{b}$?

Question 2

Which equation correctly isolates $\mathbf{x}$ in $A\mathbf{x}=\mathbf{b}$ when $A$ is invertible?

Question 3

Solve the system represented by $\begin{bmatrix}1&1\\1&-1\end{bmatrix}\mathbf{x}=\begin{bmatrix}5\\1\end{bmatrix}$.

Question 4

If $\det(A)=0$, what can you conclude about $A^{-1}$?

Question 5

For a square matrix $A$, which fact guarantees that the system $A\mathbf{x}=\mathbf{b}$ has exactly one solution for every $\mathbf{b}$?