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.
- Top left element:
- Top right element:
- Bottom left element:
- Bottom right element:
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
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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