Row Equivalence/Examples
Jump to navigation
Jump to search
Examples of Row Equivalence
Arbitrary Example $1$
Let $\mathbf A$ be the matrix defined as:
- $\mathbf A := \begin {bmatrix} 1 & 0 & -1 & 1 \\ 2 & 1 & 0 & 1 \\ -1 & 1 & 0 & -2 \end {bmatrix}$
Let $\mathbf B$ be the matrix defined as:
- $\mathbf B := \begin {bmatrix} 1 & 0 & -1 & 1 \\ -1 & 1 & 0 & 2 \\ 0 & 3 & 0 & 5 \end {bmatrix}$
Then $\mathbf A$ and $\mathbf B$ are row equivalent.
Arbitrary Example $2$
Let $\mathbf A$ be the matrix defined as:
- $\mathbf A := \begin {bmatrix} 1 & 0 & -1 \\ 2 & 1 & 0 \\ 1 & -1 & 1 \end {bmatrix}$
Let $\mathbf B$ be the matrix defined as:
- $\mathbf B := \begin {bmatrix} 3 & -1 & 1 \\ 0 & 2 & 1 \\ 1 & -1 & 1 \end {bmatrix}$
Then $\mathbf A$ and $\mathbf B$ are row equivalent.
Arbitrary Example $3$
Let $\mathbf A$ be the matrix defined as:
- $\mathbf A := \begin {bmatrix}
1 & -1 & 1 & 2 \\
-2 & 3 & 0 & 1 \\
1 & 0 & -1 & 3 \\
\end {bmatrix}$
Let $\mathbf B$ be the matrix defined as:
- $\mathbf B := \begin {bmatrix}
0 & -1 & 2 & 3 \\ 1 & 2 & -1 & 0 \\
-2 & -5 & 4 & 3 \\ \end {bmatrix}$
Then $\mathbf A$ and $\mathbf B$ are not row equivalent.