If we have a 2x2 matrix being added to a 2x2 matrix, what type of matrix will the result be?

When you add two \(2 \times 2\) matrices, the result will also be a \(2 \times 2\) matrix. This is because matrix addition is performed element-wise, and the dimensions of the matrices must be the same for addition to be defined.

For example, if you have:
\[
A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}, \quad B = \begin{pmatrix} e & f \\ g & h \end{pmatrix}
\]
Then the sum of \(A\) and \(B\) will be:
\[
A + B = \begin{pmatrix} a+e & b+f \\ c+g & d+h \end{pmatrix}
\]
The resulting matrix is also \(2 \times 2\).

Would you like a more detailed explanation on matrix addition or any specific questions about matrix operations?

Here are some related questions you may find interesting:
1. What is matrix scalar multiplication?
2. How do you multiply two matrices of different dimensions?
3. What is the identity matrix for a \(2 \times 2\) matrix?
4. How do you find the determinant of a \(2 \times 2\) matrix?
5. What are the properties of matrix addition?

**Tip:** Matrix operations require that dimensions align. For addition, both matrices must have the same dimensions.

Understand how to add two 2x2 matrices using element-wise addition. This example shows how the dimensions of the matrices remain the same, resulting in another 2x2 matrix. Learn key concepts of matrix operations in linear algebra, suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation