Math Problem Statement
Given the non-square matrix A = [[10, 6, 0, 0, 0, 1], [0, 3, 12, 0, 0, 0], [0, 0, 1, 0, 0, 0], [8, -7, 0, 3, 9, 0], [1, 18, 1, 0, 0, 0]], calculate det(A).
Solution
The matrix provided in the image is:
10 & 6 & 0 & 0 & 0 & 1 \\ 0 & 3 & 12 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 8 & -7 & 0 & 3 & 9 & 0 \\ 1 & 18 & 1 & 0 & 0 & 0 \end{bmatrix}$$ The task is to calculate the determinant of this $$5 \times 5$$ matrix. I'll compute the determinant for you. numpy as np # Define the matrix A A = np.array([ [10, 6, 0, 0, 0, 1], [0, 3, 12, 0, 0, 0], [0, 0, 1, 0, 0, 0], [8, -7, 0, 3, 9, 0], [1, 18, 1, 0, 0, 0] ]) # Compute the determinant det_A = np.linalg.det(A) det_AIt appears there was an issue with the determinant calculation because the matrix provided is not square (it has dimensions $$5 \times 6$$). Only square matrices have determinants. Would you like to verify if part of the matrix was intended to be excluded, or clarify further? Alternatively, I can assist with any other related calculations or transformations. --- ### Follow-up questions: 1. Would you like to extract any specific square submatrix from this matrix to compute its determinant? 2. Should I assist with other properties of this $$5 \times 6$$ matrix, such as its rank? 3. Are you interested in understanding the determinant concept better for non-square matrices (generalized cases)? 4. Do you want to perform a row or column operation on this matrix? 5. Should I convert this matrix into a square form by removing or adding rows/columns? **Tip:** Determinants are defined only for square matrices ($$n \times n$$). Always verify the matrix dimensions before proceeding with determinant calculations!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Determinants
Square Matrix Properties
Formulas
Determinant of a square matrix formula
Theorems
Properties of Determinants
Definition of Determinants for Square Matrices
Suitable Grade Level
Grades 10-12