Math Problem Statement
If A = [[-2, 1, 3], [0, 4, -1]] and B = [[2, 1], [-3, 0], [4, -5]], then find AB and BA.
Solution
from PIL import Image import pytesseract
Load the image
image_path = "/mnt/data/1732384307003zo63mctk.jpg" image = Image.open(image_path)
Perform OCR to extract text
extracted_text = pytesseract.image_to_string(image)
extracted_text'then find AB and BA,\n\n''then find AB and BA,\n\n'successThe question requires finding the matrix products and . The matrices and are given as:
-2 & 1 & 3 \\ 0 & 4 & -1 \end{bmatrix}, \quad B = \begin{bmatrix} 2 & 1 \\ -3 & 0 \\ 4 & -5 \end{bmatrix}.$$ I will calculate $$AB$$ and $$BA$$ step by step.import numpy as np # Define the matrices A = np.array([[-2, 1, 3], [0, 4, -1]]) B = np.array([[2, 1], [-3, 0], [4, -5]]) # Compute AB and BA AB = np.dot(A, B) try: BA = np.dot(B, A) # BA may not be computable due to incompatible dimensions except ValueError: BA = "Not computable (dimensions mismatch)" AB, BA(array([[ 5, -17], [-16, 5]]), array([[ -4, 6, 5], [ 6, -3, -9], [ -8, -16, 17]]))(array([[ 5, -17], [-16, 5]]), array([[ -4, 6, 5], [ 6, -3, -9], [ -8, -16, 17]]))successThe matrix products are as follows: $$AB = \begin{bmatrix} 5 & -17 \\ -16 & 5 \end{bmatrix}, \quad BA = \begin{bmatrix} -4 & 6 & 5 \\ 6 & -3 & -9 \\ -8 & -16 & 17 \end{bmatrix}.$$ Let me know if you'd like a detailed step-by-step explanation or have any questions! ### Related Questions: 1. How do you verify if two matrices can be multiplied? 2. What are the properties of matrix multiplication? 3. Can $$AB \neq BA$$ in general? Why or why not? 4. What is the rank of $$AB$$? 5. How would the dimensions of $$AB$$ change if $$A$$ and $$B$$ were transposed? ### Tip: Always check the dimensions of matrices before performing operations to ensure compatibility!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Multiplication
Linear Algebra
Formulas
Matrix multiplication formula C[i][j] = Σ A[i][k] * B[k][j]
Theorems
Associativity of matrix multiplication
Non-commutativity of matrix multiplication
Suitable Grade Level
Grades 11-12 or Undergraduate