Math Problem Statement
Определитель матрицы A = (7 1 5, 7 1 5, 7 0 3) равен...
Solution
The image you uploaded contains a task related to calculating the determinant of a matrix . The matrix is presented as:
7 & 1 & 5 \\ 7 & 1 & 5 \\ 7 & 0 & 3 \end{pmatrix}$$ To find the determinant of a 3x3 matrix, we can use the formula: $$\text{det}(A) = a(ei - fh) - b(di - fg) + c(dh - eg)$$ For the matrix $$A$$, where: $$A = \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix}$$ Substituting the elements from the matrix: $$a = 7, b = 1, c = 5, d = 7, e = 1, f = 5, g = 7, h = 0, i = 3$$ Let's calculate the determinant now. numpy as np # Define the matrix A = np.array([[7, 1, 5], [7, 1, 5], [7, 0, 3]]) # Calculate the determinant of the matrix det_A = np.linalg.det(A) det_AThe determinant of the matrix $$A$$ is 0. This means that the matrix is singular, meaning it doesn't have an inverse. Would you like further details on how to interpret this result or work through another problem? Here are some related questions: 1. What does it mean for a matrix to be singular? 2. How can you check if a matrix is invertible? 3. What is the role of the determinant in solving systems of linear equations? 4. How do you find the inverse of a 2x2 matrix? 5. Can the determinant be used in eigenvalue problems? Tip: Always check for matrix properties like symmetry or singularity before proceeding with certain operations like inversion.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Determinant
Formulas
det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)
Theorems
Determinant of a 3x3 matrix
Suitable Grade Level
Grades 10-12