```julia
using RowEchelon
using Latexify

rref([1 2 3; 4 5 6])

display(latexify(rref([1 2 3; 4 5 6])))

display(latexify(rref([1 2 3; 4 5 6])))
```


\begin{equation}
\left[
\begin{array}{ccc}
1.0 & 0.0 & -1.0 \\
0.0 & 1.0 & 2.0 \\
\end{array}
\right]
\end{equation}




\begin{equation}
\left[
\begin{array}{ccc}
1.0 & 0.0 & -1.0 \\
0.0 & 1.0 & 2.0 \\
\end{array}
\right]
\end{equation}




```julia
# The Four Subspaces for A
using RowEchelon
using Latexify

A = [1 3 5 0 7;
     0 0 0 1 2;
     1 3 5 1 9]

At = transpose(A)
display(A)
display(rref(A))

display("+++++++++++A Transpose+++++++++++")
display(At)
display(latexify(rref(At)))
```


    3×5 Matrix{Int64}:
     1  3  5  0  7
     0  0  0  1  2
     1  3  5  1  9



    3×5 Matrix{Float64}:
     1.0  3.0  5.0  0.0  7.0
     0.0  0.0  0.0  1.0  2.0
     0.0  0.0  0.0  0.0  0.0



    "+++++++++++A Transpose+++++++++++"



    5×3 transpose(::Matrix{Int64}) with eltype Int64:
     1  0  1
     3  0  3
     5  0  5
     0  1  1
     7  2  9



\begin{equation}
\left[
\begin{array}{ccc}
1.0 & 0.0 & 1.0 \\
0.0 & 1.0 & 1.0000000000000002 \\
0.0 & 0.0 & 0.0 \\
0.0 & 0.0 & 0.0 \\
0.0 & 0.0 & 0.0 \\
\end{array}
\right]
\end{equation}




```julia
A = [1 2 3;
     1 2 3;
     2 5 8]
display(A)
display(latexify(rref(A)))
```


    3×3 Matrix{Int64}:
     1  2  3
     1  2  3
     2  5  8



\begin{equation}
\left[
\begin{array}{ccc}
1.0 & 0.0 & -1.0 \\
0.0 & 1.0 & 2.0 \\
0.0 & 0.0 & 0.0 \\
\end{array}
\right]
\end{equation}




```julia
using RowEchelon
using Latexify

A = [1 2 3 1;
     1 1 2 1;
     1 2 3 1]
display(transpose(A))
transpose(A) * [-1,0,1]

```


    4×3 transpose(::Matrix{Int64}) with eltype Int64:
     1  1  1
     2  1  2
     3  2  3
     1  1  1





    4-element Vector{Int64}:
     0
     0
     0
     0




```julia
using 
```

af912b3454a244ba4f9f087833c5b6920041172e
ipynb
Jupyter Notebook
julia/matrix/.ipynb_checkpoints/Matrix-checkpoint.ipynb
xiongxin/playground
9f23862b35c00b810e20f2e1e661142c024baa33
MIT
julia/matrix/.ipynb_checkpoints/Matrix-checkpoint.ipynb
xiongxin/playground
9f23862b35c00b810e20f2e1e661142c024baa33
MIT
julia/matrix/.ipynb_checkpoints/Matrix-checkpoint.ipynb
xiongxin/playground
9f23862b35c00b810e20f2e1e661142c024baa33
MIT
Qwen/Qwen-72B
1. YES
2. YES