Math Problem Statement
Calculate the determinant of the matrix A = [[1, 1, 2], [0, 1, -1], [-2, -2, -4]] and choose the correct option.
Solution
from PIL import Image import pytesseract
Open the image file
img_path = '/mnt/data/17325679334683wg1g4y0.jpg' img = Image.open(img_path)
Use OCR to extract text
extracted_text = pytesseract.image_to_string(img) extracted_text''''successThe text extraction did not succeed. However, I can manually analyze the mathematical content visible in the image you provided.
The problem asks for the determinant of matrix :
1 & 1 & 2 \\ 0 & 1 & -1 \\ -2 & -2 & -4 \end{pmatrix}$$ Let me calculate the determinant for you.import numpy as np # Define the matrix A A = np.array([[1, 1, 2], [0, 1, -1], [-2, -2, -4]]) # Calculate the determinant of A det_A = np.linalg.det(A) det_A0.00.0successThe determinant of the given matrix $$A$$ is $$\mathbf{0}$$. This implies that the matrix is singular, meaning it does not have an inverse. Let me know if you'd like more details or have further questions! ### Related Questions: 1. How do you calculate the determinant of a 3x3 matrix manually? 2. What does a determinant of 0 signify in linear algebra? 3. Can a matrix with a determinant of 0 be used to solve systems of equations? 4. How can row operations affect the calculation of the determinant? 5. What are the applications of determinants in geometry and physics? ### Tip: Always check if a matrix is singular (determinant = 0) before attempting to find its inverse!Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Algebra
Determinants
Matrix Operations
Formulas
Determinant of a 3x3 matrix: det(A) = a(ei − fh) − b(di − fg) + c(dh − eg)
Theorems
Laplace Expansion for Determinants
Suitable Grade Level
Undergraduate or Advanced High School (Grades 11-12)