Math Problem Statement
Echelonnee cette matrice Et reduit
Echelonnez cette matrice et réduisez-la
Solution
To transform the matrix into its echelon form and reduced row echelon form, I'll first write down the given matrix and work step-by-step.
The matrix is:
1 & 1 & 1 & 1 \\ 1 & 2 & -1 & 2 \\ 0 & 1 & -1 & 2 \end{bmatrix}$$ ### Step 1: Transform to Row Echelon Form 1. Keep the first row as is since the pivot at (1,1) is already 1. 2. Use row operations to eliminate entries below the pivot: - $$R_2 \gets R_2 - R_1$$ - $$R_3 \gets R_3$$ $$\begin{bmatrix} 1 & 1 & 1 & 1 \\ 0 & 1 & -2 & 1 \\ 0 & 1 &-1 & 2 \\ \end { theLet me redo this.The given matrix $$A$$ is: \[ A = \begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & 2 & -1 & 2 \\ 0 & 1 & -1 & 2 \end{bmatrix}$$ ### Step 1: Row Echelon Form (REF) 1. Keep $$R_1$$ as is: $$\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & 2 & -1 & 2 \\ 0 & 1 & -1 & 2 \end{bmatrix}$$ 2. Eliminate $$R_{2,1}$$: $$R_2 \to R_2 - R_1$$: $$R_2 = \begin{bmatrix} 0 & 1 & -2 & 1 \end{bmatrix}$$ New matrix: $$\begin{bmatrix} 1 & 1 & 1 & 1 \\ 0 & 1 & -2 & 1 \\ 0 & 1 & -1 & 2 \end{bmatrix}$$ 3. Eliminate $$R_{3,2}$$ using \(R_1,/ matrixAsk a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Row Echelon Form
Reduced Row Echelon Form
Formulas
Row reduction rules: R_i → R_i + cR_j
Matrix transformation operations
Theorems
Gaussian Elimination
Elementary Row Operations
Suitable Grade Level
Undergraduate Level (Linear Algebra Course)