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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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Find Determinant Formula (3x3)

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Choose the correct formula for the determinant of this matrix based on expanding the first row

∣P∣=a11⋅∣M11∣−a12⋅∣M12∣+a13⋅∣M13∣P=[525284115]\begin{vmatrix}P\end{vmatrix} = a_{11} \cdot \begin{vmatrix}M_{11}\end{vmatrix} - a_{12} \cdot \begin{vmatrix}M_{12}\end{vmatrix} + a_{13} \cdot \begin{vmatrix}M_{13}\end{vmatrix} \\P = \left[ {\begin{array} {ccc} 5 & 2 & 5 \\ 2 & 8 & 4 \\ 1 & 1 & 5 \end{array} } \right]

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Matrices - Find Determinant Formula (3x3) Worksheet

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Math worksheet on 'Matrices - Find Determinant Formula (3x3) (Level 1)'. Part of a broader unit on 'Matrices' Learn online: app.mobius.academy/math/units/matrices/
1
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 - 1 times 28 + 1 times 12 + 1 times 0
c A LaTex expression showing - 4 times 14 - 1 times 18 + 5 times 0
d A LaTex expression showing - 4 times 28 + 1 times 14 + 5 times 0
e A LaTex expression showing - 4 times 28 + 1 times 12 + 5 times 0
f A LaTex expression showing - 4 times 28 + 1 times 10 + 5 times 0
2
Choose the correct formula for the determinant of this matrix based on expanding the first row
A LaTex expression showing \begin{vmatrix}P\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} \\P = \left[ {\begin{array} {ccc} 5 & 2 & 5 \\ 2 & 8 & 4 \\ 1 & 1 & 5 \end{array} } \right]
a A LaTex expression showing 5 times 36 - 2 times 4 + 5 times 0
b A LaTex expression showing 5 times 36 - 2 times 9 - 5 times 7
c A LaTex expression showing 5 times 36 - 2 times 6 - 5 times 6
d A LaTex expression showing 5 times 36 + 2 times 6 - 5 times 6
e A LaTex expression showing 1 times 36 - 1 times 6 - 1 times 6
f A LaTex expression showing 5 times 36 - 2 times 6 + 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}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} 3 & 0 & 1 \\ 5 & 2 & 0 \\ 9 & 1 & 7 \end{array} } \right]
a A LaTex expression showing 3 times 14 - 0 times 35 - 1 times 13
b A LaTex expression showing 1 times 14 - 1 times 35 - 1 times 13
c A LaTex expression showing 3 times 14 + 0 times 35 - 1 times 13
d A LaTex expression showing 3 times 14 - 0 times 49 - 1 times 14
e A LaTex expression showing 3 times 14 - 0 times 21 - 1 times 16
f A LaTex expression showing 3 times 14 - 0 times 46 - 1 times 16
4
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 33 - 8 times 39 + 0 times 5
b A LaTex expression showing - 9 times 25 + 8 times 35 + 0 times 5
c A LaTex expression showing - 9 times 25 + 8 times 49 + 0 times 8
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 - 1 times 25 + 1 times 35 + 1 times 5
5
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} 6 & 0 & 5 \\ 6 & 6 & 8 \\ 7 & 9 & 0 \end{array} } \right]
a A LaTex expression showing - 6 times 72 + 0 times 56 + 5 times 12
b A LaTex expression showing - 6 times 72 + 0 times 84 + 5 times 16
c A LaTex expression showing - 6 times 72 + 0 times 62 + 5 times 8
d A LaTex expression showing - 6 times 72 - 0 times 56 + 5 times 12
e A LaTex expression showing - 6 times 72 + 0 times 62 + 5 times 0
f A LaTex expression showing - 6 times 72 + 0 times 84 + 5 times 14
6
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} 7 & 4 & 6 \\ 6 & 6 & 8 \\ 0 & 1 & 5 \end{array} } \right]
a A LaTex expression showing 7 times 20 - 4 times 30 + 6 times 7
b A LaTex expression showing 7 times 22 - 4 times 30 + 6 times 6
c A LaTex expression showing 7 times 22 - 4 times 39 + 6 times 3
d A LaTex expression showing 1 times 22 - 1 times 30 + 1 times 6
e A LaTex expression showing 7 times 22 - 4 times 33 + 6 times 8
f A LaTex expression showing 7 times 22 + 4 times 15 + 6 times 6
7
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} 3 & 9 & 7 \\ 6 & 2 & 6 \\ 3 & 5 & 6 \end{array} } \right]
a A LaTex expression showing - 3 times 18 - 9 times 16 + 7 times 26
b A LaTex expression showing - 1 times 18 - 1 times 18 + 1 times 24
c A LaTex expression showing - 3 times 18 - 9 times 18 + 7 times 24
d A LaTex expression showing - 3 times 25 + 9 times 18 + 7 times 24
e A LaTex expression showing - 3 times 18 - 9 times 18 + 7 times 34
f A LaTex expression showing - 3 times 14 - 9 times 18 + 7 times 31