# Linear algebra Row picture and Column picture for system of linear equations

I am presently going through Strang's linear algebra book in which he explains row picture and column picture for a system of linear equations as such

For example: $$\begin{cases} 2x + 3y = 5 \\ 4x + 7y = 9 \end{cases}$$

are two lines in row picture and in column picture they are 2-d vectors in the 2-D space

similarly, $$\begin{cases} 2u + v + w = 5 \\ 4u - 6v = -2 \\ -2u + 7v + 2w = 9 \end{cases}$$

in row picture these represent 3 planes ( the second equation still a plane with $w$ taking any value) and from column picture consists 3-d vectors of 3-D space

What can i infer for a system of linear equations with $n$ equations and $m$ unknowns such as this $$\begin{cases} 2x + 7y = 9 \\ 3x + 8y = 11 \\ 3x - 2y = 4 \\ x + y = 6 \end{cases}$$

what does the row picture shows for this system of linear equations ? Column picture is in 4D space.

I am new to linear algebra, please correct me if my understanding is wrong. Thanks

You can think that the system represents the intersection of four hyperplanes ( isomorphic to $3-D$ spaces) and the solution $P=(x_0,y_0,t_0,s_0)$ is the common point of these hyperplanes.
The ''columns'' interpretation can be a linear transformation from a $2-D$ space to a $4-D$ space.