Math Problem Statement
resolver la determinante
resolver la determinante
Solution
To find the determinant of the 3x3 matrix given in the image:
1 & 4 & 9 \\ 7 & 2 & 5 \\ 6 & 8 & 3 \end{pmatrix}$$ The determinant of a 3x3 matrix is calculated as: $$\text{det}(A) = a(ei - fh) - b(di - fg) + c(dh - eg)$$ For matrix $$A$$: $$\text{det}(A) = 1 \cdot (2 \cdot 3 - 5 \cdot 8) - 4 \cdot (7 \cdot 3 - 5 \cdot 6) + 9 \cdot (7 \cdot 8 - 2 \cdot 6)$$ Breaking it down: - $$2 \cdot 3 = 6$$ - $$5 \cdot 8 = 40$$ - $$7 \cdot 3 = 21$$ - $$5 \cdot 6 = 30$$ - $$7 \cdot 8 = 56$$ - $$2 \cdot 6 = 12$$ So: $$\text{det}(A) = 1 \cdot (6 - 40) - 4 \cdot (21 - 30) + 9 \cdot (56 - 12)$$ $$\text{det}(A) = 1 \cdot (-34) - 4 \cdot (-9) + 9 \cdot 44$$ $$\text{det}(A) = -34 + 36 + 396$$ $$\text{det}(A) = 398$$ Thus, the determinant of matrix $$A$$ is $$\text{det}(A) = 398$$. Would you like further details or have any questions? Here are some related questions you might consider: 1. How does the determinant help in understanding the properties of a matrix? 2. What is the geometric interpretation of a matrix determinant? 3. Can the determinant be used to determine if a matrix is invertible? 4. What is the relationship between the determinant and the eigenvalues of a matrix? 5. How does changing one element of the matrix affect the determinant? **Tip:** When calculating the determinant of a matrix, it's often helpful to expand along a row or column with the most zeros to simplify calculations.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Algebra
Determinants
Formulas
det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)
Theorems
Determinant of a 3x3 Matrix
Suitable Grade Level
Grades 11-12