Math Problem Statement

\left[ \begin{array}{cc}

-2 & 0

\\

3 & -2

\end{array} \right]+\left[ \begin{array}{cc}

3 & -1

\\

2 & 0

\end{array} \right]=

Solution

To add two matrices, we add their corresponding elements. Given matrices:

[ \left[ \begin{array}{cc} -2 & 0 \ 3 & -2 \end{array} \right] + \left[ \begin{array}{cc} 3 & -1 \ 2 & 0 \end{array} \right] ]

we add each element in the first matrix to the corresponding element in the second matrix.

  1. Top left element: 2+3=1-2 + 3 = 1
  2. Top right element: 0+(1)=10 + (-1) = -1
  3. Bottom left element: 3+2=53 + 2 = 5
  4. Bottom right element: 2+0=2-2 + 0 = -2

So, the resulting matrix is:

1 & -1 \\ 5 & -2 \end{array} \right]$$ ### Final Answer: $$\left[ \begin{array}{cc} 1 & -1 \\ 5 & -2 \end{array} \right]$$ Would you like more details on matrix operations or have any questions? Here are some related questions to explore further: 1. How do we perform matrix multiplication, and how does it differ from matrix addition? 2. What are the properties of matrix addition and scalar multiplication? 3. How do you determine the inverse of a $$2 \times 2$$ matrix? 4. What is the determinant of a matrix, and how does it affect matrix properties? 5. How can we solve a system of linear equations using matrix methods? **Tip:** Always ensure that matrices are of the same dimensions before performing addition or subtraction.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Matrix Addition
Linear Algebra

Formulas

Matrix addition: For matrices A and B, (A + B)_{ij} = A_{ij} + B_{ij}

Theorems

Properties of Matrix Addition

Suitable Grade Level

Grades 10-12