Math Problem Statement

Add two matrices that have a whole number entrie.

Solution

To add two matrices with whole number entries, each element in the first matrix is added to the corresponding element in the second matrix. Here’s an example:

If we have: A=(2357)andB=(4168)A = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \quad \text{and} \quad B = \begin{pmatrix} 4 & 1 \\ 6 & 8 \end{pmatrix}

Then their sum, C=A+BC = A + B, is calculated as: C=(2+43+15+67+8)=(641115)C = \begin{pmatrix} 2+4 & 3+1 \\ 5+6 & 7+8 \end{pmatrix} = \begin{pmatrix} 6 & 4 \\ 11 & 15 \end{pmatrix}

Would you like details on matrix addition or have any questions?

Here are some related questions to explore:

  1. How do you subtract two matrices?
  2. What are the conditions for matrix addition to be valid?
  3. How do you multiply two matrices?
  4. What is a scalar multiplication in matrices?
  5. How does matrix addition apply in real-world problems?

Tip: Always ensure matrices are of the same dimensions before adding them.

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Math Problem Analysis

Mathematical Concepts

Matrix Addition
Whole Numbers
Linear Algebra

Formulas

Element-wise matrix addition: C[i][j] = A[i][j] + B[i][j]

Theorems

Matrix Addition Property: Matrices must be of the same dimensions for element-wise addition

Suitable Grade Level

Grades 9-12