Math Problem Statement

If A = [[2, -1], [4, 0]] and B = [[5, 2], [-3, 2]], find 3A - 2B.

Solution

The solution to 3A2B3A - 2B is the matrix:

3A2B=[47184]3A - 2B = \begin{bmatrix} -4 & -7 \\ 18 & -4 \end{bmatrix}

Would you like further details on how this was calculated?

Here are 5 related questions to consider:

  1. What are the properties of matrix addition and scalar multiplication?
  2. How do you compute the product of a scalar with a matrix?
  3. What is the determinant of the resulting matrix 3A2B3A - 2B?
  4. How can we check if the matrix 3A2B3A - 2B is invertible?
  5. How do matrices behave under addition and multiplication in terms of linear transformations?

Tip: When working with matrix operations, always check the matrix dimensions to ensure they can be added, subtracted, or multiplied!

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Math Problem Analysis

Mathematical Concepts

Matrix Algebra
Scalar Multiplication
Matrix Subtraction

Formulas

3A - 2B
Scalar multiplication: c * A = [[c*a11, c*a12], [c*a21, c*a22]]
Matrix subtraction: A - B = [[a11-b11, a12-b12], [a21-b21, a22-b22]]

Theorems

Matrix Addition and Subtraction Properties
Scalar Multiplication in Matrices

Suitable Grade Level

Grades 9-10