Math Problem Statement

Add two matrices that have a whole number entrie.

Solution

To add two matrices with whole number entries, you simply add each corresponding element from one matrix to the other.

Let's consider two example matrices with whole number entries:

A=(1357911131517)A = \begin{pmatrix} 1 & 3 & 5 \\ 7 & 9 & 11 \\ 13 & 15 & 17 \end{pmatrix} and B=(24681012141618)B = \begin{pmatrix} 2 & 4 & 6 \\ 8 & 10 & 12 \\ 14 & 16 & 18 \end{pmatrix}

The sum of matrices AA and BB, denoted as A+BA + B, is found by adding corresponding entries:

A+B=(1+23+45+67+89+1011+1213+1415+1617+18)=(3711151923273135)A + B = \begin{pmatrix} 1+2 & 3+4 & 5+6 \\ 7+8 & 9+10 & 11+12 \\ 13+14 & 15+16 & 17+18 \end{pmatrix} = \begin{pmatrix} 3 & 7 & 11 \\ 15 & 19 & 23 \\ 27 & 31 & 35 \end{pmatrix}

The resulting matrix A+BA + B is:

(3711151923273135)\begin{pmatrix} 3 & 7 & 11 \\ 15 & 19 & 23 \\ 27 & 31 & 35 \end{pmatrix}

Would you like more details on matrix operations, or do you have other questions?

Here are 5 related questions to consider:

  1. What happens if the matrices have different dimensions?
  2. How would subtraction of matrices differ from addition?
  3. Can matrices with decimal or fractional entries be added similarly?
  4. What are practical applications of matrix addition?
  5. How do you add matrices in programming languages like Python?

Tip: When adding matrices, make sure they are of the same size (same number of rows and columns), or else addition is undefined.

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Math Problem Analysis

Mathematical Concepts

Matrix Addition
Linear Algebra

Formulas

A + B = (a_ij + b_ij) for each element in corresponding positions

Theorems

Matrix Addition Property (Element-wise addition)

Suitable Grade Level

Grades 9-12