Math Problem Statement
Solve
Perform the row operations on the matrix and write the resulting matrix. Replace R2 by R1 + R2. The given matrix is: [1 0 2] [-1 1 3]
Solution
Let's solve this matrix problem by following the row operation as instructed. We are given the matrix:
1 & 0 & 2 \\ -1 & 1 & 3 \end{pmatrix}$$ The instruction is to replace $$R_2$$ (the second row) with $$R_1 + R_2$$. Let's compute that: - First row: $$R_1 = [1, 0, 2]$$ - Second row: $$R_2 = [-1, 1, 3]$$ Now, adding $$R_1$$ and $$R_2$$: \[ R_1 + R_2 = [1 + (-1), 0 + 1, 2 + 3] = [0, 1, 5] \] Thus, the new matrix after the operation becomes: $$\begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 5 \end{pmatrix}$$ This corresponds to the answer: $$\boxed{\begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 5 \end{pmatrix}}$$ Let me know if you'd like more details or have any questions! --- **Related questions**: 1. How can row operations be used to solve systems of equations? 2. What is the significance of reduced row echelon form (RREF) in matrix algebra? 3. How does matrix addition differ from matrix multiplication? 4. How are elementary row operations useful in finding matrix inverses? 5. Can Gaussian elimination be applied to non-square matrices? **Tip**: When performing row operations, always check for consistency in the dimensions of the matrix and ensure that each element operation is correctly applied across the entire row.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Matrix Row Operations
Matrix Addition
Formulas
Matrix addition: R2 = R1 + R2
Theorems
Elementary Row Operations
Suitable Grade Level
Grades 9-12