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# Thread: What is a geometric interpretation of all these information?

1. Hey!!

We have the tableau $\begin{pmatrix} \left.\begin{matrix} 1 & 0 & \alpha \\ 0 & 1 & \beta \\ 0 & 0 & 0 \end{matrix}\right|\begin{matrix} c\\ d\\ 0 \end{matrix} \end{pmatrix}$

Since there is a zero-row, we conclude that the column vectors are linearly dependent.

The number of linearly independent row- and column vectors is the same. And from the tableau we get that there are $2$ linearly independent row- and column vectors. Therefore the dimension of the the vector space spanned by the solumn vectors is $2$. And this is also equal to the rank of the matrix.

The dimension of the solution space is equal to the numer of free variables, so $1$, right?

Is everything correct so far?

What is a geometric interpretation of all these information? Do we get that two column vectors are either a multiple of each other or they are on the same line? Or is there also an other interpretation?

2.