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Matrices

Create Augmented Matrix (3x3) (Level 1)

This math topic involves the creation of augmented matrices from given 3x3 matrices to facilitate the process of matrix inversion. Each question presents a 3x3 matrix, and the task is to correctly augment it with an identity matrix, transforming it into a 3x4 matrix. Multiple choice answers are provided, where the correct option represents the matrix accurately augmented to initiate inversion. This exercise is foundational for understanding matrix operations, particularly the inversion process, which is critical in solving systems of linear equations.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Matrices - Create Augmented Matrix (3x3) Worksheet

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Matrices - Create Augmented Matrix (3x3)
1
Created an augmented matrix from this matrix to start the process of inverting it
A LaTex expression showing \left[ {\begin{array} {ccc} 7 & 6 & 8 \\ 0 & 4 & 2 \\ 1 & 9 & 8 \end{array} } \right]
a A LaTex expression showing undefined
b A LaTex expression showing \left[ {\begin{array} {cccc} 0 & 0 & 0 & \vert & 7 & 6 & 8 \\ 0 & 0 & 0 & \vert & 0 & 4 & 2 \\ 0 & 0 & 0 & \vert & 1 & 9 & 8 \end{array} } \right]
c A LaTex expression showing \left[ {\begin{array} {cccc} 7 & 6 & 8 & \vert & 0 & 0 & 1 \\ 0 & 4 & 2 & \vert & 0 & 1 & 0 \\ 1 & 9 & 8 & \vert & 1 & 0 & 0 \end{array} } \right]
d A LaTex expression showing \left[ {\begin{array} {cccc} 7 & 6 & 8 & \vert & 0 & 0 & 0 \\ 0 & 4 & 2 & \vert & 0 & 0 & 0 \\ 1 & 9 & 8 & \vert & 0 & 0 & 0 \end{array} } \right]
e A LaTex expression showing \left[ {\begin{array} {cccc} 7 & 6 & 8 & \vert & 1 & 1 & 1 \\ 0 & 4 & 2 & \vert & 1 & 1 & 1 \\ 1 & 9 & 8 & \vert & 1 & 1 & 1 \end{array} } \right]
f A LaTex expression showing \left[ {\begin{array} {cccc} 7 & 6 & 8 & \vert & 1 & 0 & 0 \\ 0 & 4 & 2 & \vert & 0 & 1 & 0 \\ 1 & 9 & 8 & \vert & 0 & 0 & 1 \end{array} } \right]
2
Created an augmented matrix from this matrix to start the process of inverting it
A LaTex expression showing \left[ {\begin{array} {ccc} 0 & 6 & 8 \\ 0 & 4 & 2 \\ 4 & 6 & 6 \end{array} } \right]
a A LaTex expression showing \left[ {\begin{array} {cccc} 0 & 0 & 0 & \vert & 0 & 6 & 8 \\ 0 & 0 & 0 & \vert & 0 & 4 & 2 \\ 0 & 0 & 0 & \vert & 4 & 6 & 6 \end{array} } \right]
b A LaTex expression showing \left[ {\begin{array} {cccc} 0 & 6 & 8 & \vert & 0 & 0 & 1 \\ 0 & 4 & 2 & \vert & 0 & 1 & 0 \\ 4 & 6 & 6 & \vert & 1 & 0 & 0 \end{array} } \right]
c A LaTex expression showing \left[ {\begin{array} {cccc} 0 & 6 & 8 & \vert & 1 & 0 & 0 \\ 0 & 4 & 2 & \vert & 0 & 1 & 0 \\ 4 & 6 & 6 & \vert & 0 & 0 & 1 \end{array} } \right]
d A LaTex expression showing \left[ {\begin{array} {cccc} 0 & 6 & 8 & \vert & 0 & 0 & 0 \\ 0 & 4 & 2 & \vert & 0 & 0 & 0 \\ 4 & 6 & 6 & \vert & 0 & 0 & 0 \end{array} } \right]
e A LaTex expression showing \left[ {\begin{array} {cccc} 1 & 1 & 1 & \vert & 0 & 6 & 8 \\ 1 & 1 & 1 & \vert & 0 & 4 & 2 \\ 1 & 1 & 1 & \vert & 4 & 6 & 6 \end{array} } \right]
f A LaTex expression showing undefined
3
Created an augmented matrix from this matrix to start the process of inverting it
A LaTex expression showing \left[ {\begin{array} {ccc} 3 & 8 & 4 \\ 6 & 4 & 9 \\ 2 & 8 & 9 \end{array} } \right]
a A LaTex expression showing \left[ {\begin{array} {cccc} 3 & 8 & 4 & \vert & 1 & 1 & 1 \\ 6 & 4 & 9 & \vert & 1 & 1 & 1 \\ 2 & 8 & 9 & \vert & 1 & 1 & 1 \end{array} } \right]
b A LaTex expression showing \left[ {\begin{array} {cccc} 3 & 8 & 4 & \vert & 0 & 0 & 0 \\ 6 & 4 & 9 & \vert & 0 & 0 & 0 \\ 2 & 8 & 9 & \vert & 0 & 0 & 0 \end{array} } \right]
c A LaTex expression showing \left[ {\begin{array} {cccc} 1 & 0 & 0 & \vert & 3 & 8 & 4 \\ 0 & 1 & 0 & \vert & 6 & 4 & 9 \\ 0 & 0 & 1 & \vert & 2 & 8 & 9 \end{array} } \right]
d A LaTex expression showing \left[ {\begin{array} {cccc} 1 & 1 & 1 & \vert & 3 & 8 & 4 \\ 1 & 1 & 1 & \vert & 6 & 4 & 9 \\ 1 & 1 & 1 & \vert & 2 & 8 & 9 \end{array} } \right]
e A LaTex expression showing \left[ {\begin{array} {cccc} 3 & 8 & 4 & \vert & 1 & 0 & 0 \\ 6 & 4 & 9 & \vert & 0 & 1 & 0 \\ 2 & 8 & 9 & \vert & 0 & 0 & 1 \end{array} } \right]
f A LaTex expression showing \left[ {\begin{array} {cccc} 0 & 0 & 0 & \vert & 3 & 8 & 4 \\ 0 & 0 & 0 & \vert & 6 & 4 & 9 \\ 0 & 0 & 0 & \vert & 2 & 8 & 9 \end{array} } \right]
4
Created an augmented matrix from this matrix to start the process of inverting it
A LaTex expression showing \left[ {\begin{array} {ccc} 7 & 0 & 5 \\ 7 & 2 & 0 \\ 2 & 2 & 6 \end{array} } \right]
a A LaTex expression showing \left[ {\begin{array} {cccc} 1 & 1 & 1 & \vert & 7 & 0 & 5 \\ 1 & 1 & 1 & \vert & 7 & 2 & 0 \\ 1 & 1 & 1 & \vert & 2 & 2 & 6 \end{array} } \right]
b A LaTex expression showing undefined
c A LaTex expression showing \left[ {\begin{array} {cccc} 7 & 0 & 5 & \vert & 1 & 1 & 1 \\ 7 & 2 & 0 & \vert & 1 & 1 & 1 \\ 2 & 2 & 6 & \vert & 1 & 1 & 1 \end{array} } \right]
d A LaTex expression showing \left[ {\begin{array} {cccc} 7 & 0 & 5 & \vert & 1 & 0 & 0 \\ 7 & 2 & 0 & \vert & 0 & 1 & 0 \\ 2 & 2 & 6 & \vert & 0 & 0 & 1 \end{array} } \right]
e A LaTex expression showing \left[ {\begin{array} {cccc} 7 & 0 & 5 & \vert & 0 & 0 & 0 \\ 7 & 2 & 0 & \vert & 0 & 0 & 0 \\ 2 & 2 & 6 & \vert & 0 & 0 & 0 \end{array} } \right]
f A LaTex expression showing \left[ {\begin{array} {cccc} 0 & 0 & 0 & \vert & 7 & 0 & 5 \\ 0 & 0 & 0 & \vert & 7 & 2 & 0 \\ 0 & 0 & 0 & \vert & 2 & 2 & 6 \end{array} } \right]
5
Created an augmented matrix from this matrix to start the process of inverting it
A LaTex expression showing \left[ {\begin{array} {ccc} 6 & 6 & 3 \\ 7 & 9 & 1 \\ 9 & 4 & 6 \end{array} } \right]
a A LaTex expression showing \left[ {\begin{array} {cccc} 6 & 6 & 3 & \vert & 1 & 0 & 0 \\ 7 & 9 & 1 & \vert & 0 & 1 & 0 \\ 9 & 4 & 6 & \vert & 0 & 0 & 1 \end{array} } \right]
b A LaTex expression showing \left[ {\begin{array} {cccc} 0 & 0 & 1 & \vert & 6 & 6 & 3 \\ 0 & 1 & 0 & \vert & 7 & 9 & 1 \\ 1 & 0 & 0 & \vert & 9 & 4 & 6 \end{array} } \right]
c A LaTex expression showing undefined
d A LaTex expression showing \left[ {\begin{array} {cccc} 6 & 6 & 3 & \vert & 0 & 0 & 1 \\ 7 & 9 & 1 & \vert & 0 & 1 & 0 \\ 9 & 4 & 6 & \vert & 1 & 0 & 0 \end{array} } \right]
e A LaTex expression showing \left[ {\begin{array} {cccc} 6 & 6 & 3 & \vert & 1 & 1 & 1 \\ 7 & 9 & 1 & \vert & 1 & 1 & 1 \\ 9 & 4 & 6 & \vert & 1 & 1 & 1 \end{array} } \right]
f A LaTex expression showing \left[ {\begin{array} {cccc} 1 & 1 & 1 & \vert & 6 & 6 & 3 \\ 1 & 1 & 1 & \vert & 7 & 9 & 1 \\ 1 & 1 & 1 & \vert & 9 & 4 & 6 \end{array} } \right]
6
Created an augmented matrix from this matrix to start the process of inverting it
A LaTex expression showing \left[ {\begin{array} {ccc} 3 & 7 & 1 \\ 4 & 5 & 2 \\ 0 & 5 & 3 \end{array} } \right]
a A LaTex expression showing \left[ {\begin{array} {cccc} 3 & 7 & 1 & \vert & 1 & 1 & 1 \\ 4 & 5 & 2 & \vert & 1 & 1 & 1 \\ 0 & 5 & 3 & \vert & 1 & 1 & 1 \end{array} } \right]
b A LaTex expression showing \left[ {\begin{array} {cccc} 3 & 7 & 1 & \vert & 0 & 0 & 0 \\ 4 & 5 & 2 & \vert & 0 & 0 & 0 \\ 0 & 5 & 3 & \vert & 0 & 0 & 0 \end{array} } \right]
c A LaTex expression showing \left[ {\begin{array} {cccc} 3 & 7 & 1 & \vert & 1 & 0 & 0 \\ 4 & 5 & 2 & \vert & 0 & 1 & 0 \\ 0 & 5 & 3 & \vert & 0 & 0 & 1 \end{array} } \right]
d A LaTex expression showing \left[ {\begin{array} {cccc} 3 & 7 & 1 & \vert & 0 & 0 & 1 \\ 4 & 5 & 2 & \vert & 0 & 1 & 0 \\ 0 & 5 & 3 & \vert & 1 & 0 & 0 \end{array} } \right]
e A LaTex expression showing \left[ {\begin{array} {cccc} 1 & 0 & 0 & \vert & 3 & 7 & 1 \\ 0 & 1 & 0 & \vert & 4 & 5 & 2 \\ 0 & 0 & 1 & \vert & 0 & 5 & 3 \end{array} } \right]
f A LaTex expression showing \left[ {\begin{array} {cccc} 1 & 1 & 1 & \vert & 3 & 7 & 1 \\ 1 & 1 & 1 & \vert & 4 & 5 & 2 \\ 1 & 1 & 1 & \vert & 0 & 5 & 3 \end{array} } \right]
7
Created an augmented matrix from this matrix to start the process of inverting it
A LaTex expression showing \left[ {\begin{array} {ccc} 3 & 2 & 3 \\ 9 & 1 & 3 \\ 8 & 4 & 8 \end{array} } \right]
a A LaTex expression showing \left[ {\begin{array} {cccc} 0 & 0 & 1 & \vert & 3 & 2 & 3 \\ 0 & 1 & 0 & \vert & 9 & 1 & 3 \\ 1 & 0 & 0 & \vert & 8 & 4 & 8 \end{array} } \right]
b A LaTex expression showing \left[ {\begin{array} {cccc} 3 & 2 & 3 & \vert & 0 & 0 & 1 \\ 9 & 1 & 3 & \vert & 0 & 1 & 0 \\ 8 & 4 & 8 & \vert & 1 & 0 & 0 \end{array} } \right]
c A LaTex expression showing \left[ {\begin{array} {cccc} 3 & 2 & 3 & \vert & 1 & 0 & 0 \\ 9 & 1 & 3 & \vert & 0 & 1 & 0 \\ 8 & 4 & 8 & \vert & 0 & 0 & 1 \end{array} } \right]
d A LaTex expression showing \left[ {\begin{array} {cccc} 1 & 1 & 1 & \vert & 3 & 2 & 3 \\ 1 & 1 & 1 & \vert & 9 & 1 & 3 \\ 1 & 1 & 1 & \vert & 8 & 4 & 8 \end{array} } \right]
e A LaTex expression showing \left[ {\begin{array} {cccc} 0 & 0 & 0 & \vert & 3 & 2 & 3 \\ 0 & 0 & 0 & \vert & 9 & 1 & 3 \\ 0 & 0 & 0 & \vert & 8 & 4 & 8 \end{array} } \right]
f A LaTex expression showing \left[ {\begin{array} {cccc} 1 & 0 & 0 & \vert & 3 & 2 & 3 \\ 0 & 1 & 0 & \vert & 9 & 1 & 3 \\ 0 & 0 & 1 & \vert & 8 & 4 & 8 \end{array} } \right]
8
Created an augmented matrix from this matrix to start the process of inverting it
A LaTex expression showing \left[ {\begin{array} {ccc} 6 & 2 & 8 \\ 2 & 2 & 5 \\ 1 & 2 & 6 \end{array} } \right]
a A LaTex expression showing \left[ {\begin{array} {cccc} 6 & 2 & 8 & \vert & 0 & 0 & 0 \\ 2 & 2 & 5 & \vert & 0 & 0 & 0 \\ 1 & 2 & 6 & \vert & 0 & 0 & 0 \end{array} } \right]
b A LaTex expression showing \left[ {\begin{array} {cccc} 0 & 0 & 1 & \vert & 6 & 2 & 8 \\ 0 & 1 & 0 & \vert & 2 & 2 & 5 \\ 1 & 0 & 0 & \vert & 1 & 2 & 6 \end{array} } \right]
c A LaTex expression showing \left[ {\begin{array} {cccc} 6 & 2 & 8 & \vert & 1 & 1 & 1 \\ 2 & 2 & 5 & \vert & 1 & 1 & 1 \\ 1 & 2 & 6 & \vert & 1 & 1 & 1 \end{array} } \right]
d A LaTex expression showing \left[ {\begin{array} {cccc} 6 & 2 & 8 & \vert & 1 & 0 & 0 \\ 2 & 2 & 5 & \vert & 0 & 1 & 0 \\ 1 & 2 & 6 & \vert & 0 & 0 & 1 \end{array} } \right]
e A LaTex expression showing \left[ {\begin{array} {cccc} 0 & 0 & 0 & \vert & 6 & 2 & 8 \\ 0 & 0 & 0 & \vert & 2 & 2 & 5 \\ 0 & 0 & 0 & \vert & 1 & 2 & 6 \end{array} } \right]
f A LaTex expression showing \left[ {\begin{array} {cccc} 1 & 1 & 1 & \vert & 6 & 2 & 8 \\ 1 & 1 & 1 & \vert & 2 & 2 & 5 \\ 1 & 1 & 1 & \vert & 1 & 2 & 6 \end{array} } \right]