Math Problem Statement
תחשב לי את הדטרמיננטה
תחשב לי את הדטרמיננטה
Solution
The matrix you provided is a 4x4 matrix:
1 & 5 & 1 & 3 \\ 0 & 0 & 6 & 1 \\ 1 & 0 & 3 & 9 \\ 0 & 0 & 4 & 2 \end{bmatrix}$$ To calculate the determinant of this matrix, I will use cofactor expansion or row reduction methods. Let's compute it. I'll go ahead and calculate the determinant for you now. numpy as np # Define the matrix matrix = np.array([[1, 5, 1, 3], [0, 0, 6, 1], [1, 0, 3, 9], [0, 0, 4, 2]]) # Calculate the determinant det = np.linalg.det(matrix) detThe determinant of the given matrix is approximately 40. Would you like further explanation on how the determinant was calculated or have any other questions related to this? Here are some related questions you might find interesting: 1. How do I calculate the determinant of a 4x4 matrix manually? 2. What is the cofactor expansion method for calculating determinants? 3. How does row reduction work for finding the determinant of a matrix? 4. What happens to the determinant when you swap two rows or columns? 5. How do matrix transformations relate to determinants? **Tip:** The determinant of a matrix provides information about its invertibility. If the determinant is zero, the matrix is singular (not invertible).Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Determinants
Formulas
Determinant of a 4x4 matrix using cofactor expansion
Row reduction determinant calculation
Theorems
Properties of determinants
Cofactor expansion theorem
Suitable Grade Level
Grades 11-12 or Undergraduate Level