Math Problem Statement
Solution
To find the determinant of a 3x3 matrix, , we can use the formula:
where the matrix is:
For the matrix given in your image:
Let's identify each element in terms of etc.:
Step-by-Step Determinant Calculation:
Breaking it down:
- First term:
- Second term:
- Third term: Since the third term has , it contributes to the determinant.
Adding these results:
Answer:
Would you like further details or have any questions?
Here are 5 related questions that expand on this topic:
- How would the determinant calculation change if one of the entries in matrix were different?
- What does the determinant of a matrix tell us about the matrix?
- How can we determine if a 3x3 matrix is invertible using its determinant?
- How would we calculate the determinant of a 4x4 matrix?
- Can the determinant be used to find the area or volume spanned by vectors?
Tip: The sign of each term in the cofactor expansion alternates. For a 3x3 matrix, it follows the pattern for each element in the first row.
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Determinants
Formulas
Determinant of 3x3 matrix: det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)
Theorems
Cofactor Expansion for Determinants
Suitable Grade Level
Grades 10-12
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