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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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 \left[ {\begin{array} {ccc} 9 & 2 & 2 \\ 5 & 6 & 3 \\ 9 & 4 & 8 \end{array} } \right]
a A LaTex expression showing 1 times 36 - 1 times 13 - 1 times 34
b A LaTex expression showing 9 times 54 - 2 times 13 - 2 times 37
c A LaTex expression showing 9 times 36 - 2 times 13 - 2 times 34
d A LaTex expression showing 9 times 36 - 2 times 16 - 2 times 31
e A LaTex expression showing 9 times 36 - 2 times 7 - 2 times 37
f A LaTex expression showing 9 times 36 + 2 times 13 - 2 times 34
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} 8 & 9 & 6 \\ 6 & 0 & 6 \\ 9 & 9 & 3 \end{array} } \right]
a A LaTex expression showing - 8 times 65 - 9 times 43 + 6 times 54
b A LaTex expression showing - 8 times 54 + 9 times 36 + 6 times 54
c A LaTex expression showing - 8 times 49 - 9 times 18 + 6 times 54
d A LaTex expression showing - 8 times 43 - 9 times 22 + 6 times 54
e A LaTex expression showing - 8 times 54 - 9 times 36 + 6 times 54
f A LaTex expression showing - 8 times 38 + 9 times 36 + 6 times 59
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} 0 & 2 & 4 \\ 0 & 1 & 8 \\ 4 & 4 & 9 \end{array} } \right]
a A LaTex expression showing - 0 times 23 + 2 times 32 - 4 times 4
b A LaTex expression showing - 0 times 23 - 2 times 0 - 4 times 5
c A LaTex expression showing - 0 times 23 + 2 times 32 - 4 times 6
d A LaTex expression showing - 0 times 23 - 2 times 32 - 4 times 4
e A LaTex expression showing - 0 times 23 + 2 times 45 - 4 times 2
f A LaTex expression showing - 0 times 23 + 2 times 26 - 4 times 4
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} 0 & 3 & 6 \\ 4 & 2 & 8 \\ 9 & 3 & 2 \end{array} } \right]
a A LaTex expression showing - 0 times 20 + 3 times 77 - 6 times 5
b A LaTex expression showing - 1 times 20 + 1 times 64 - 1 times 6
c A LaTex expression showing - 0 times 20 + 3 times 64 - 6 times 6
d A LaTex expression showing - 0 times 20 + 3 times 38 - 6 times 8
e A LaTex expression showing - 0 times 20 - 3 times 64 - 6 times 6
f A LaTex expression showing - 0 times 28 - 3 times 38 - 6 times 6
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} 9 & 4 & 4 \\ 8 & 7 & 0 \\ 5 & 3 & 2 \end{array} } \right]
a A LaTex expression showing 9 times 14 + 4 times 16 - 4 times 11
b A LaTex expression showing 9 times 18 + 4 times 19 - 4 times 11
c A LaTex expression showing 9 times 14 - 4 times 16 - 4 times 11
d A LaTex expression showing 9 times 21 - 4 times 16 - 4 times 9
e A LaTex expression showing 1 times 14 - 1 times 16 - 1 times 11
f A LaTex expression showing 9 times 0 - 4 times 16 - 4 times 8
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 & 2 & 2 \\ 7 & 8 & 6 \\ 0 & 2 & 5 \end{array} } \right]
a A LaTex expression showing 2 times 28 - 2 times 42 + 2 times 7
b A LaTex expression showing 2 times 28 + 2 times 35 + 2 times 14
c A LaTex expression showing 2 times 28 - 2 times 35 + 2 times 14
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 28 + 2 times 20
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} 9 & 7 & 0 \\ 5 & 2 & 1 \\ 6 & 3 & 6 \end{array} } \right]
a A LaTex expression showing 9 times 9 - 7 times 24 + 0 times 3
b A LaTex expression showing 9 times 5 + 7 times 24 + 0 times 3
c A LaTex expression showing 9 times 7 + 7 times 17 + 0 times 3
d A LaTex expression showing 9 times 9 + 7 times 29 + 0 times 3
e A LaTex expression showing 9 times 7 - 7 times 24 + 0 times 3
f A LaTex expression showing 9 times 9 + 7 times 24 + 0 times 3
8
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 & 0 \\ 9 & 3 & 9 \\ 4 & 6 & 5 \end{array} } \right]
a A LaTex expression showing - 7 times 39 - 0 times 9 + 0 times 42
b A LaTex expression showing - 7 times 39 - 0 times 5 + 0 times 55
c A LaTex expression showing - 7 times 39 - 0 times 11 + 0 times 46
d A LaTex expression showing - 7 times 39 - 0 times 0 + 0 times 25
e A LaTex expression showing - 1 times 39 - 1 times 9 + 1 times 42
f A LaTex expression showing - 7 times 39 - 0 times 12 + 0 times 34