Math Problem Statement
Find the matrix expression 4A + 6B where A = [[9, 5], [5, 2]] and B = [[6, -3], [-2, 6]].
Solution
Let's solve the given problem.
We are given the matrices:
and we are tasked with finding .
Step 1: Multiply each matrix by its scalar.
-
Multiply by 4:
-
Multiply by 6:
Step 2: Add the results of and .
Step 3: Perform the element-wise addition.
Final Answer:
Let me know if you would like a step-by-step breakdown of matrix operations!
Here are 5 related questions for further exploration:
- What is the determinant of the resulting matrix ?
- How would the calculation change if and were 3x3 matrices?
- Can you find and then scale it by a factor of 5?
- What are the eigenvalues of and individually?
- If and represented transformations, what is the combined transformation represented by ?
Tip: When adding or multiplying matrices, ensure their dimensions match for the operation to be valid!
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Math Problem Analysis
Mathematical Concepts
Matrix Algebra
Matrix Scalar Multiplication
Matrix Addition
Formulas
4A = 4 * A
6B = 6 * B
A + B = A[i][j] + B[i][j]
Theorems
Matrix Addition
Scalar Multiplication of Matrices
Suitable Grade Level
Grades 9-12