Exercises for Question Type 8: Using the inverse matrix, if it exists, to solve for a system of linear equations - IB | RevisionDojo

Exercises for Question Type 8: Using the inverse matrix, if it exists, to solve for a system of linear equations - IB | RevisionDojo

Question 1

Skill question

Solve the system using the inverse matrix method:

\begin{pmatrix}1 & 1\\2 & 3\end{pmatrix}\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}1\\4\end{pmatrix}

Question 2

Skill question

Solve the system using the inverse matrix method:

\begin{pmatrix}3 & 2\\5 & -4\end{pmatrix}\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}7\\-1\end{pmatrix}

Question 3

Skill question

Solve the system using the inverse matrix method:

\begin{pmatrix}2 & 1\\3 & -1\end{pmatrix} \begin{pmatrix}x\\y\end{pmatrix} = \begin{pmatrix}5\\4\end{pmatrix}

Question 4

Skill question

Solve the system using the inverse matrix method:

\begin{pmatrix}3 & 0 & 1\\1 & -2 & 3\\5 & 1 & 2\end{pmatrix}\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}4\\-1\\10\end{pmatrix}

Question 5

Skill question

Solve the system using the inverse matrix method:

\begin{pmatrix}3 & 1 & 2\\4 & 2 & 1\\2 & 1 & 3\end{pmatrix}\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}5\\10\\9\end{pmatrix}

Question 6

Skill question

Solve the system using the inverse matrix method:

\begin{pmatrix}1 & 2 & 3\\2 & -1 & 1\\3 & 1 & -2\end{pmatrix}\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}6\\3\\2\end{pmatrix}

Question 7

Skill question

Solve the system using the inverse matrix method:

\begin{pmatrix}1 & 3 & 2\\2 & -1 & 1\\3 & 2 & -1\end{pmatrix}\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}8\\1\\3\end{pmatrix}

Question 8

Skill question

Solve the system using the inverse matrix method:

\begin{pmatrix}1 & 2 & -1\\2 & -1 & 3\\-1 & 4 & 2\end{pmatrix}\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}3\\7\\1\end{pmatrix}

Question 9

Skill question

Solve the system using the inverse matrix method:

\begin{pmatrix}2 & 1 & 3\\1 & -1 & 1\\3 & 4 & -1\end{pmatrix}\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}12\\3\\5\end{pmatrix}

Question 10

Skill question

Solve the system using the inverse matrix method:

\begin{pmatrix}1 & 2 & 1\\2 & -1 & 1\\3 & 1 & -2\end{pmatrix}\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}14\\3\\1\end{pmatrix}

Question 11

Skill question

Solve the system using the inverse matrix method:

\begin{pmatrix}4 & 1 & -1\\-2 & 3 & 2\\1 & -1 & 4\end{pmatrix}\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}0\\5\\2\end{pmatrix}

Question 12

Skill question

Solve the system with fractional coefficients using the inverse matrix method:

\begin{pmatrix}\tfrac12 & 1 & -1\\1 & -\tfrac13 & 2\\2 & 1 & \tfrac14\end{pmatrix}\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}2\\1\\3\end{pmatrix}