Find Determinant Formula (3x3) (Level 2)

This math topic focuses on finding the determinant of a 3x3 matrix by expanding the first row. Students are provided with several 3x3 matrices and are asked to select the correct determinant formula from multiple choices. Each question includes an array and several algebraic expressions representing potential solutions for the determinant calculation. This helps reinforce skills in matrix manipulation and determinant computation, important topics in the broader study of 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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Math worksheet on 'Matrices - Find Determinant Formula (3x3) (Level 2)'. 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 \left[ {\begin{array} {ccc} 2 & 2 & 2 \\ 7 & 8 & 6 \\ 0 & 2 & 5 \end{array} } \right]
a A LaTex expression showing 2 times 28 + 2 times 35 + 2 times 14
b A LaTex expression showing 2 times 28 - 2 times 35 + 2 times 14
c A LaTex expression showing 2 times 28 - 2 times 28 + 2 times 20
d A LaTex expression showing 2 times 28 - 2 times 25 + 2 times 20
e A LaTex expression showing 1 times 28 - 1 times 35 + 1 times 14
f A LaTex expression showing 2 times 28 - 2 times 42 + 2 times 7
2
Choose the correct formula for the determinant of this matrix based on expanding the first row
A LaTex expression showing \left[ {\begin{array} {ccc} 7 & 0 & 1 \\ 1 & 6 & 7 \\ 3 & 9 & 4 \end{array} } \right]
a A LaTex expression showing - 7 times 27 - 0 times 15 - 1 times 9
b A LaTex expression showing - 7 times 39 + 0 times 10 - 1 times 9
c A LaTex expression showing - 7 times 39 + 0 times 14 - 1 times 5
d A LaTex expression showing - 7 times 39 + 0 times 20 - 1 times 5
e A LaTex expression showing - 7 times 39 + 0 times 17 - 1 times 9
f A LaTex expression showing 7 times 0 - 0 times 15 - 1 times 9
3
Choose the correct formula for the determinant of this matrix based on expanding the first row
A LaTex expression showing \left[ {\begin{array} {ccc} 5 & 7 & 0 \\ 4 & 9 & 9 \\ 5 & 7 & 3 \end{array} } \right]
a A LaTex expression showing - 5 times 36 + 7 times 50 - 0 times 20
b A LaTex expression showing - 5 times 36 + 7 times 33 - 0 times 17
c A LaTex expression showing - 5 times 36 - 7 times 33 - 0 times 17
d A LaTex expression showing - 5 times 36 + 7 times 20 - 0 times 12
e A LaTex expression showing - 5 times 36 + 7 times 33 - 0 times 10
f A LaTex expression showing - 5 times 36 + 7 times 40 - 0 times 17
4
Choose the correct formula for the determinant of this matrix based on expanding the first row
A LaTex expression showing \left[ {\begin{array} {ccc} 5 & 1 & 7 \\ 7 & 1 & 3 \\ 1 & 4 & 7 \end{array} } \right]
a A LaTex expression showing - 5 times 4 - 1 times 46 + 7 times 0
b A LaTex expression showing - 5 times 5 - 1 times 69 + 7 times 32
c A LaTex expression showing - 1 times 5 - 1 times 46 + 1 times 27
d A LaTex expression showing - 5 times 6 + 1 times 0 + 7 times 27
e A LaTex expression showing - 5 times 5 - 1 times 46 + 7 times 27
f A LaTex expression showing - 5 times 5 - 1 times 64 + 7 times 38
5
Choose the correct formula for the determinant of this matrix based on expanding the first row
A LaTex expression showing \left[ {\begin{array} {ccc} 6 & 4 & 3 \\ 1 & 7 & 5 \\ 1 & 8 & 3 \end{array} } \right]
a A LaTex expression showing - 6 times 19 - 4 times 2 + 3 times 1
b A LaTex expression showing - 6 times 27 + 4 times 2 + 3 times 1
c A LaTex expression showing - 6 times 19 + 4 times 2 + 3 times 1
d A LaTex expression showing - 6 times 29 - 4 times 2 + 3 times 1
e A LaTex expression showing - 6 times 19 + 4 times 1 + 3 times 1
f A LaTex expression showing - 6 times 21 + 4 times 2 + 3 times 0
6
Choose the correct formula for the determinant of this matrix based on expanding the first row
A LaTex expression showing \left[ {\begin{array} {ccc} 2 & 3 & 9 \\ 3 & 2 & 2 \\ 1 & 1 & 3 \end{array} } \right]
a A LaTex expression showing 2 times 4 + 3 times 7 + 9 times 1
b A LaTex expression showing 2 times 2 + 3 times 7 + 9 times 1
c A LaTex expression showing 1 times 4 - 1 times 7 + 1 times 1
d A LaTex expression showing 2 times 4 - 3 times 7 + 9 times 1
e A LaTex expression showing 2 times 4 - 3 times 10 + 9 times 1
f A LaTex expression showing 2 times 4 - 3 times 6 + 9 times 1
7
Choose the correct formula for the determinant of this matrix based on expanding the first row
A LaTex expression showing \left[ {\begin{array} {ccc} 8 & 9 & 3 \\ 6 & 2 & 6 \\ 9 & 4 & 0 \end{array} } \right]
a A LaTex expression showing - 8 times 24 + 9 times 54 + 3 times 6
b A LaTex expression showing - 8 times 24 - 9 times 70 + 3 times 6
c A LaTex expression showing - 8 times 24 - 9 times 54 + 3 times 6
d A LaTex expression showing - 8 times 24 + 9 times 32 + 3 times 8
e A LaTex expression showing - 8 times 22 - 9 times 81 + 3 times 6
f A LaTex expression showing - 8 times 24 + 9 times 32 + 3 times 9