Math Problem Statement

Solve for 2A + 5B where A = \( \begin{bmatrix} -8 & -4 \\ -10 & -4 \end{bmatrix} \) and B = \( \begin{bmatrix} -7 & -8 \\ -5 & -10 \end{bmatrix} \).

Solution

sympy import Matrix

Define the matrices A and B

A = Matrix([[-8, -4], [-10, -4]]) B = Matrix([[-7, -8], [-5, -10]])

Compute 2A + 5B

result = 2 * A + 5 * B resultThe solution to 2A+5B2A + 5B is:

-51 & -48 \\ -45 & -58 \end{bmatrix}$$ ### Do you want a step-by-step explanation? Let me know! --- ### Related Questions: 1. How do you calculate scalar multiplication of a matrix? 2. How is matrix addition performed element by element? 3. What are the properties of matrix addition and scalar multiplication? 4. Can you explain matrix multiplication with an example? 5. What is the determinant of a $$2 \times 2$$ matrix and how is it calculated? ### Tip: Always perform scalar multiplication before addition when solving matrix operations.

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Math Problem Analysis

Mathematical Concepts

Matrix Operations
Scalar Multiplication
Matrix Addition

Formulas

Scalar multiplication: cA = \( c \cdot a_{ij} \)
Matrix addition: A + B = \( a_{ij} + b_{ij} \)

Theorems

Matrix operations are performed element by element.

Suitable Grade Level

Grades 9-11