Question

In Section 2.2 of the book "Introduction to Linear Algebra" by Gilbert Strang, under the topic "Breakdown of Elimination" it is written, "The column picture shows the two columns (1,3) and (-2,-6) in the same direction." Now my question is that the vectors mentioned are in opposite directions, or did I miss something while learning vectors? @ShadowLegendX @imqwerty

Answer 1

@phi @baru

Answer 2

@Directrix

Answer 3

sometimes people call that the "sense" of the vector
but if you have a vector pointing in the direction v
then we say any scalar multiple of v is in the same "direction"
for a negative scalar, that allows us to point in the "opposite" direction, but
for our purposes we say it's the same direction but opposite sense.

Answer 4

this two vector is parallel,so they don't meet.for this we can't find a solution for it.this is called elimination failed or target of elimination is failed.we do elimination to solving a system.