Math Problem Statement
solve matrix
Reduce the following matrix to its row reduced echelon form:
\begin{pmatrix}
1 & 1 & 3 \\
3 & 5 & 8 \\
2 & -1 & 3
\end{pmatrix}
Solution
The reduced row echelon form (RREF) of the given matrix
1 & 1 & 3 \\ 3 & 5 & 8 \\ 2 & -1 & 3 \end{pmatrix}$$ is: $$\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}$$ This is the identity matrix, indicating that the original matrix is invertible and has full rank. Would you like to go over any specific steps or need further explanation? Here are 5 related questions to explore: 1. How do you determine if a matrix is invertible using row reduction? 2. What is the significance of reduced row echelon form in solving linear systems? 3. How can RREF be used to find the rank of a matrix? 4. What are the properties of a matrix that lead to a diagonal RREF? 5. How do you interpret free variables when solving a system using RREF? **Tip:** The RREF is particularly useful for solving systems of linear equations, as it simplifies the matrix to a form where solutions can be easily read off.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Operations
Row Reduction
Row Echelon Form
Formulas
Row reduction operations for matrix manipulation
Gaussian elimination
Theorems
Invertible Matrix Theorem
Rank-Nullity Theorem
Suitable Grade Level
College Level (Introductory Linear Algebra)