Math Problem Statement

Let A = [[-7, -2], [4, -8]] and B = [[2, 8], [3, -2]]. Find 4A + 4B.

Solution

The result of 4A+4B4A + 4B is:

4A+4B=[20242840]4A + 4B = \begin{bmatrix} -20 & 24 \\ 28 & -40 \end{bmatrix}

Do you want any further details or clarifications?

Here are some related questions to deepen your understanding:

  1. How do you perform matrix addition and scalar multiplication?
  2. What are the properties of matrix addition that make it commutative?
  3. How does scalar multiplication affect both individual elements and the overall matrix?
  4. Can you find the determinant of the resulting matrix 4A+4B4A + 4B?
  5. How would you compute the inverse of a matrix (if it exists)?

Tip: Always remember that matrix addition is element-wise, and scalar multiplication affects each element of the matrix individually.

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Math Problem Analysis

Mathematical Concepts

Matrix Addition
Scalar Multiplication

Formulas

Matrix addition: A + B = [[a11 + b11, a12 + b12], [a21 + b21, a22 + b22]]
Scalar multiplication: kA = [[k * a11, k * a12], [k * a21, k * a22]]

Theorems

Associative property of matrix addition
Distributive property of scalar multiplication over matrix addition

Suitable Grade Level

Grades 9-12