Fundamentals of Matrix Algebra, 2011a

Chapter 2
Matrix Arithmec
S To draw ⃗x −⃗y, we will first draw −⃗y and then apply the Parallelogram
Law to add ⃗x to −⃗y. See Figure 2.11.
⃗y
. ⃗x
⃗x −⃗y
−⃗y
.
.
Figure 2.11: Vectors ⃗x, ⃗y and ⃗x − ⃗y in Example 36
In Figure 2.12, we redraw Figure 2.11 from Example 36 but remove the gray vectors
that tend to add cluer, and we redraw the vector⃗x−⃗y doed so that it starts from the
p of ⃗y. 9 Note that the doed version of ⃗x −⃗y points from ⃗y to ⃗x. This is a “shortcut”
to drawing ⃗x − ⃗y; simply draw the vector that starts at the p of ⃗y and ends at the p
of ⃗x. This is important so we make it a Key Idea.
⃗y
⃗x −⃗y
⃗x
.
-⃗y
⃗x −⃗y
.
Figure 2.12: Redrawing vector ⃗x
− ⃗y
. Key Idea 6 Vector Subtracon
To draw the vector⃗x −⃗y, draw⃗x . and⃗y so that they have the
same origin. The vector ⃗x − ⃗y is the vector that starts from
the p of⃗y and points to the p of ⃗x.
Let’s pracce this once more with a quick example.
. Example 37 .Let ⃗x and⃗y be as in Figure ?? (a). Draw ⃗x −⃗y.
S We simply apply Key Idea 6: we draw an arrow from⃗y to⃗x. We do
so in Figure 2.13; ⃗x −⃗y is dashed.
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9 Remember that we can draw vectors starng from anywhere.