Math Problem Statement

Выполнить умножение матриц B*A. В ответе указать сумму элементов первого столбца.

Solution

The problem involves matrix multiplication BAB \cdot A, where:

\begin{pmatrix} 1 & 3 & -1 \\ 7 & -2 & 3 \\ 8 & 3 & 0 \end{pmatrix}, \quad B = \begin{pmatrix} 8 & 1 & 3 \\ -7 & 3 & 4 \\ 2 & 4 & -1 \end{pmatrix}.$$ We need to compute $$B \cdot A$$, then find the sum of the elements of the first column of the resulting matrix. Let's calculate this. numpy as np # Define matrices A and B A = np.array([[1, 3, -1], [7, -2, 3], [8, 3, 0]]) B = np.array([[8, 1, 3], [-7, 3, 4], [2, 4, -1]]) # Compute B * A result = np.dot(B, A) # Sum of elements in the first column of the resulting matrix sum_first_column = np.sum(result[:, 0]) result, sum_first_columnThe result of the matrix multiplication $$B \cdot A$$ is: $$\begin{pmatrix} 39 & 31 & -5 \\ 46 & -15 & 16 \\ 22 & -5 & 10 \end{pmatrix}.$$ The sum of the elements of the first column is: $$39 + 46 + 22 = 107.$$ If you have any questions or want further details, let me know! ### Related Questions: 1. How do we determine the dimensions of the resulting matrix after multiplication? 2. Why does matrix multiplication involve summing products of rows and columns? 3. Can $$A \cdot B$$ be computed, and would it yield the same result? 4. What are some practical applications of matrix multiplication in real-world problems? 5. What properties of matrix multiplication make it non-commutative? ### Tip: Always verify the dimensions of matrices to ensure that the multiplication is defined before proceeding!

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Math Problem Analysis

Mathematical Concepts

Matrix Multiplication
Linear Algebra

Formulas

C[i,j] = Σ(A[i,k] * B[k,j]) for matrix multiplication

Theorems

Matrix Multiplication Definition

Suitable Grade Level

Grades 10-12