Determinant 2×2 Matrix Problems with Answers

In order to get better at solving 2×2 matrix determinants, work through these ten (10) practice problems. The more you practice, the better you’ll get at any skill. So let’s get started!

You may use this exercise for independent practice, homework, cooperative learning, and more!

Problem 1: Find the determinant of the matrix below.

\Large{\begin{bmatrix} 2 & 5 \\ 3 & 4 \end{bmatrix}}
Answer
determinant of matrix { {2,5},{3,4} } is -7

Problem 2: Find the determinant of the matrix below.

\Large{\begin{bmatrix} 6 & 2 \\ -5 & -2 \end{bmatrix}}
Answer
the determinant of matrix { {6,2} , {-5,-2} } is -2

Problem 3: Find the determinant of the matrix below.

\Large{\begin{bmatrix} 3 & -3 \\ 2 & 1 \end{bmatrix}}
Answer
the determinant of matrix { {3,-3} , {2,1} } is 9

Problem 4: Find the determinant of the matrix below.

\Large{\begin{bmatrix} 0.5 & -2 \\ 4 & -6 \end{bmatrix}}
Answer
the determinant of matrix { {0.5,-2} , {4,-6} } is 5

Problem 5: Find the determinant of the matrix below.

\Large{\begin{bmatrix} -5 & 4 \\ -4 & 5 \end{bmatrix}}
Answer
the determinant of matrix { {-5,4} , {-4,5} } is -9

Problem 6: Find the determinant of the matrix below.

\Large{\begin{bmatrix} -9 & -0.2 \\ -10 & -0.5 \end{bmatrix}}
Answer
the determinant of matrix { {-9,-0.2} , {-10,-0.5} } is 2.5

Problem 7: Find the determinant of the matrix below.

\Large{\begin{bmatrix} -2.5 & 0.01 \\ 35 & 0.1 \end{bmatrix}}
Answer
the determinant of matrix { {-2.5,0.01} , {35,0.1} } is 2.5

Problem 8: The determinant of a 2×2 matrix is \large{2}. Find the value of \color{red}\Large{x}.

the determinant of { {-2,x}, {4,5} } is 2
Answer
the value of x that satisfies that determinant of { {-2,x), {4,5} } is 2 is -3

Therefore, \large{\color{red}\boxed{x=-3}}.


Problem 9: The determinant of a 2×2 matrix is \large{-11}. Find the value of \color{red}\large{y}.

the determinant of { {-1,2}, {y,3} } is -11
Answer
the value of y that satisfies the determinant { {-1,2}, {y,3} } =-11 is 4

Therefore, \large{\color{red}\boxed{y=4}}.


Problem 10: The determinant of a 2×2 matrix is \large{-8}. Find the value of \color{red}\large{k}.

the determinant of { {k,3}, {-9,7} } is -8
Answer
the value of k that satisfies the determinant { {k,3},{-9,7} } =-8 is -5

Therefore, \large{\color{red}\boxed{k=-5}}.


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