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Matrices

Find Determinant Formula (3x3) (Level 1)

This math topic focuses on practicing the calculation of the determinant for 3x3 matrices. Specifically, students learn to expand along the first row using the formula for the determinant. Each problem involves choosing the correct application of this formula to specific matrices. The problems serve as a component of a broader unit on matrices, aimed at improving students' skills in matrix algebra, specifically in calculating determinants of 3x3 matrices.

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

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Matrices - Find Determinant Formula (3x3) Worksheet

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Matrices - Find Determinant Formula (3x3)
1
Choose the correct formula for the determinant of this matrix based on expanding the first row
A LaTex expression showing \begin{vmatrix}N\end{vmatrix} = a sub 11 times \begin{vmatrix}M sub 11 \end{vmatrix} - a sub 12 times \begin{vmatrix}M sub 12 \end{vmatrix} + a sub 13 times \begin{vmatrix}M sub 13 \end{vmatrix} \\N = \left[ {\begin{array} {ccc} 3 & 4 & 2 \\ 6 & 7 & 8 \\ 9 & 9 & 3 \end{array} } \right]
a A LaTex expression showing - 3 times 46 - 4 times 32 - 2 times 9
b A LaTex expression showing - 3 times 51 + 4 times 54 - 2 times 9
c A LaTex expression showing - 3 times 51 + 4 times 76 - 2 times 11
d A LaTex expression showing - 3 times 56 + 4 times 54 - 2 times 9
e A LaTex expression showing - 3 times 51 - 4 times 54 - 2 times 9
f A LaTex expression showing - 3 times 66 + 4 times 54 - 2 times 10
2
Choose the correct formula for the determinant of this matrix based on expanding the first row
A LaTex expression showing \begin{vmatrix}C\end{vmatrix} = a sub 11 times \begin{vmatrix}M sub 11 \end{vmatrix} - a sub 12 times \begin{vmatrix}M sub 12 \end{vmatrix} + a sub 13 times \begin{vmatrix}M sub 13 \end{vmatrix} \\C = \left[ {\begin{array} {ccc} 4 & 1 & 5 \\ 0 & 0 & 4 \\ 3 & 7 & 1 \end{array} } \right]
a A LaTex expression showing - 4 times 28 - 1 times 12 + 5 times 0
b A LaTex expression showing - 4 times 28 + 1 times 12 + 5 times 0
c A LaTex expression showing - 4 times 28 + 1 times 10 + 5 times 0
d A LaTex expression showing - 4 times 14 - 1 times 18 + 5 times 0
e A LaTex expression showing - 1 times 28 + 1 times 12 + 1 times 0
f A LaTex expression showing - 4 times 28 + 1 times 14 + 5 times 0
3
Choose the correct formula for the determinant of this matrix based on expanding the first row
A LaTex expression showing \begin{vmatrix}Y\end{vmatrix} = a sub 11 times \begin{vmatrix}M sub 11 \end{vmatrix} - a sub 12 times \begin{vmatrix}M sub 12 \end{vmatrix} + a sub 13 times \begin{vmatrix}M sub 13 \end{vmatrix} \\Y = \left[ {\begin{array} {ccc} 4 & 7 & 2 \\ 1 & 6 & 6 \\ 9 & 9 & 4 \end{array} } \right]
a A LaTex expression showing - 4 times 21 - 7 times 55 - 2 times 45
b A LaTex expression showing - 4 times 24 - 7 times 75 - 2 times 45
c A LaTex expression showing - 4 times 30 + 7 times 50 - 2 times 68
d A LaTex expression showing - 4 times 30 + 7 times 30 + 2 times 0
e A LaTex expression showing - 4 times 30 + 7 times 50 - 2 times 45
f A LaTex expression showing - 1 times 30 + 1 times 50 - 1 times 45
4
Choose the correct formula for the determinant of this matrix based on expanding the first row
A LaTex expression showing \begin{vmatrix}D\end{vmatrix} = a sub 11 times \begin{vmatrix}M sub 11 \end{vmatrix} - a sub 12 times \begin{vmatrix}M sub 12 \end{vmatrix} + a sub 13 times \begin{vmatrix}M sub 13 \end{vmatrix} \\D = \left[ {\begin{array} {ccc} 5 & 4 & 3 \\ 0 & 4 & 1 \\ 9 & 6 & 0 \end{array} } \right]
a A LaTex expression showing - 5 times 9 - 4 times 8 - 3 times 36
b A LaTex expression showing - 5 times 6 + 4 times 9 - 3 times 36
c A LaTex expression showing - 5 times 6 + 4 times 10 - 3 times 47
d A LaTex expression showing - 5 times 6 + 4 times 12 - 3 times 32
e A LaTex expression showing - 5 times 6 - 4 times 0 - 3 times 43
f A LaTex expression showing - 1 times 6 + 1 times 9 - 1 times 36
5
Choose the correct formula for the determinant of this matrix based on expanding the first row
A LaTex expression showing \begin{vmatrix}N\end{vmatrix} = a sub 11 times \begin{vmatrix}M sub 11 \end{vmatrix} - a sub 12 times \begin{vmatrix}M sub 12 \end{vmatrix} + a sub 13 times \begin{vmatrix}M sub 13 \end{vmatrix} \\N = \left[ {\begin{array} {ccc} 9 & 8 & 0 \\ 8 & 5 & 5 \\ 7 & 5 & 0 \end{array} } \right]
a A LaTex expression showing - 9 times 25 - 8 times 35 + 0 times 5
b A LaTex expression showing - 9 times 25 + 8 times 49 + 0 times 8
c A LaTex expression showing - 1 times 25 + 1 times 35 + 1 times 5
d A LaTex expression showing - 9 times 25 + 8 times 35 + 0 times 5
e A LaTex expression showing - 9 times 38 - 8 times 18 + 0 times 5
f A LaTex expression showing - 9 times 33 - 8 times 39 + 0 times 5
6
Choose the correct formula for the determinant of this matrix based on expanding the first row
A LaTex expression showing \begin{vmatrix}M\end{vmatrix} = a sub 11 times \begin{vmatrix}M sub 11 \end{vmatrix} - a sub 12 times \begin{vmatrix}M sub 12 \end{vmatrix} + a sub 13 times \begin{vmatrix}M sub 13 \end{vmatrix} \\M = \left[ {\begin{array} {ccc} 2 & 2 & 0 \\ 8 & 6 & 0 \\ 6 & 0 & 8 \end{array} } \right]
a A LaTex expression showing 2 times 48 - 2 times 83 - 0 times 43
b A LaTex expression showing 2 times 48 + 2 times 64 - 0 times 36
c A LaTex expression showing 2 times 48 - 2 times 64 - 0 times 18
d A LaTex expression showing 2 times 48 - 2 times 64 - 0 times 36
e A LaTex expression showing 1 times 48 - 1 times 64 - 1 times 36
f A LaTex expression showing 2 times 34 - 2 times 64 - 0 times 47
7
Choose the correct formula for the determinant of this matrix based on expanding the first row
A LaTex expression showing \begin{vmatrix}M\end{vmatrix} = a sub 11 times \begin{vmatrix}M sub 11 \end{vmatrix} - a sub 12 times \begin{vmatrix}M sub 12 \end{vmatrix} + a sub 13 times \begin{vmatrix}M sub 13 \end{vmatrix} \\M = \left[ {\begin{array} {ccc} 4 & 0 & 3 \\ 2 & 9 & 2 \\ 0 & 1 & 2 \end{array} } \right]
a A LaTex expression showing 4 times 16 - 0 times 5 + 3 times 1
b A LaTex expression showing 4 times 8 + 0 times 5 + 3 times 2
c A LaTex expression showing 4 times 16 - 0 times 4 + 3 times 0
d A LaTex expression showing 4 times 16 - 0 times 4 + 3 times 2
e A LaTex expression showing 4 times 16 - 0 times 5 + 3 times 0
f A LaTex expression showing 4 times 16 - 0 times 5 + 3 times 3
8
Choose the correct formula for the determinant of this matrix based on expanding the first row
A LaTex expression showing \begin{vmatrix}B\end{vmatrix} = a sub 11 times \begin{vmatrix}M sub 11 \end{vmatrix} - a sub 12 times \begin{vmatrix}M sub 12 \end{vmatrix} + a sub 13 times \begin{vmatrix}M sub 13 \end{vmatrix} \\B = \left[ {\begin{array} {ccc} 1 & 2 & 2 \\ 3 & 7 & 8 \\ 6 & 2 & 1 \end{array} } \right]
a A LaTex expression showing - 1 times 9 + 2 times 45 - 2 times 36
b A LaTex expression showing - 1 times 9 + 2 times 27 - 2 times 43
c A LaTex expression showing - 1 times 8 - 2 times 23 - 2 times 36
d A LaTex expression showing - 1 times 9 + 1 times 45 - 1 times 36
e A LaTex expression showing - 1 times 10 - 2 times 50 - 2 times 36
f A LaTex expression showing 1 times 0 - 2 times 68 - 2 times 36