Questions 26-28 review the row and column pictures in 2,3, and 4 dimensions. 26.

Question

Questions 26-28 review the row and column pictures in 2,3, and 4 dimensions.

26.
Draw the row and column pictures for the equations x-2y=0, x+y=6

I'm not even exactly sure what "row and column pictures" means. Based off examples earlier, I guessed the column picture is just graphing the vectors (1,1) (-2,1) and the solution vector, which is 6j or (0,6)- although that seems deceivingly simple.

If what I did above is right, then that means the row picture is the graph of (1,-2) (1,1) and the solution 6i or (6,0) -- I think.

Can someone please tell me if this is correct or not, and if not, how to solve it?
There's no answer in the back, and I'd REALLY like to see this textbook appear in Cramster's database sometime soon *wink wink*.

Explanation / Answer

The row picture is drawing the graphs of the lines x-2y=0 and x+y=6 and seeing that they intersect at the point (4,2). The column picture looks at the problem in this way. x[1] +y [-2] = [0]= b [1] [1 ] [6] If we draw the vector (1,1) multiply it by 4 to get to (4,4), and then add 2 times the vector (-2,1) (which is (-4,2)), the sum of these two vectors is (0,6), which is equal to our solution vector. This shows that (4,2) is the answer to the problem. Hope this helps.

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