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Question 1

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}5\\1\\0\end{pmatrix}

[7]

Question 2

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}6\\-3\\5\end{pmatrix}

[6]

Question 3

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

\begin{pmatrix}\dfrac12 & 1 & -1\\1 & -\dfrac13 & 2\\2 & 1 & \dfrac14\end{pmatrix}\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}2\\1\\3\end{pmatrix}

[6]

Question 4

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}

[4]

Question 5

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}

[5]

Question 6

Solve systems of linear equations using the inverse matrix method.

Solve the system of linear equations 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}14\\4\\7\end{pmatrix}

[8]

Question 7

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}

[6]

Question 8

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}9\\1\\6\end{pmatrix}

[8]

Question 9

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\\2\\2\end{pmatrix}

[6]

Question 10

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}

[4]

Question 11

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}

[6]

Question 12

A system of three linear equations is represented by the matrix equation $AX = B$ .

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}

[7]

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