1. ## Algebraic Vectors

Let vector $\displaystyle m = [2, -1]$ and vector $\displaystyle b = [0, 5]$

a) Determine the components of each vector in this list:

$\displaystyle b + 3m = [6, 2]$

$\displaystyle b + 2m = [4, 3]$

$\displaystyle b + m = [2, 4]$

$\displaystyle b + 0m = [0, 5]$

$\displaystyle b - m = [-2, 6]$

$\displaystyle b - 2m = [-4, 7]$

$\displaystyle b - 3m = [-6, 8]$

b) Graph all 7 vectors in part a with tail at $\displaystyle [0, 0]$

c) Explain the pattern in the results. ------- Does this mean the graph increases or decreases 2 units for the x values and the y values goes increases or decreases 1 unit? ----------- If I'm correct, is there a correct term to use for it?

d) How would the above results be affected if vector b were replaced with each vector? ------ I don't see a pattern for the next two. . .Do I use a specific formula to find the pattern?

i) $\displaystyle b = [2,4]$

$\displaystyle b + 3m = [8, 11]$

$\displaystyle b + 2m = [8, 7]$

$\displaystyle b + m = [4, 3]$

$\displaystyle b + 0m = [2, -1]$

$\displaystyle b - m = [0, -5]$

$\displaystyle b - 2m = [-2, -9]$

$\displaystyle b - 3m = [-4, -13]$

ii) $\displaystyle b = [-1, 2]$

$\displaystyle b + 3m = [-1, 5]$

$\displaystyle b + 2m = [0, 3]$

$\displaystyle b + m = [1, 1]$

$\displaystyle b + 0m = [2, -1]$

$\displaystyle b - m = [3, -3]$

$\displaystyle b - 2m = [4, -5]$

$\displaystyle b - 3m = [5, -7]$

2. Originally Posted by Macleef
Let vector $\displaystyle m = [2, -1]$ and vector $\displaystyle b = [0, 6]$

a) Determine the components of each vector in this list:
$\displaystyle b + 3m = [6, 2]$
$\displaystyle b + 2m = [4, 3]$
$\displaystyle b + m = [2, 4]$
$\displaystyle b + 0m = [0, 5]$ ... I don't understand how you get these results
$\displaystyle b - m = [-2, 6]$
$\displaystyle b - 2m = [-4, 7]$
$\displaystyle b - 3m = [-6, 8]$
b) Graph all 7 vectors in part a with tail at $\displaystyle [0, 0]$

...
Your calculations of the coordinates of the heads of the vectors are wrong.

For instance: $\displaystyle b + 2m = (0, 6) + 2 \cdot (2, -1) = (0, 6) + (4, -2) = (4, 4)$

The heads of all vectors form the line $\displaystyle y = -\frac12 x + 6$ or written as equation with vectors:

$\displaystyle (x, y) = (0, 6) + r \cdot (2, -1)$

3. It's a typo in my part, it's b[0, 5] and not b[0, 6]

4. Originally Posted by Macleef
It's a typo in my part, it's b[0, 5] and not b[0, 6]
The heads of all vectors form the line $\displaystyle y = -\frac12 x + 5$ or written as equation with vectors:
$\displaystyle (x, y) = (0, 5) + r \cdot (2, -1)$