Fundamentals of Matrix Algebra, 2011a

2.3 Visualizing Matrix Arithmec in 2D
vectors ⃗x and⃗y. This highlights what is known as the Parallelogram Law.
1
⃗x
. ⃗y
1
Figure 2.4: Adding vectors graphically . using the Parallelogram Law
⃗y
⃗x
⃗x +⃗y
. Key Idea 5 Parallelogram Law
To draw the vector ⃗x + ⃗y, one.
can draw the parallelogram
with ⃗x and ⃗y as its sides. The vector that points from the
vertex where ⃗x and ⃗y originate to the vertex where ⃗x and ⃗y
meet is the vector ⃗x +⃗y.
Knowing all of this allows us to draw the sum of two vectors without knowing
specifically what the vectors are, as we demonstrate in the following example.
. Example 33 Consider the vectors ⃗x and ⃗y as drawn in Figure 2.5. Sketch the
vector ⃗x +⃗y.
S
⃗y
.
⃗x
.
Figure 2.5: Vectors ⃗x and ⃗y in Example 33
We’ll apply the Parallelogram Law, as given in Key Idea 5. As before, we draw⃗x +⃗y
dashed to set it apart. The result is given in Figure 2.6.
⃗x +⃗y
⃗y
.
⃗x
.
Figure 2.6: Vectors ⃗x, ⃗y and ⃗x + ⃗y in Example 33
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