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 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.Ask a new question for Free
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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