Algebraic Vectors

**Macleef** · February 13th 2008, 01:52 PM

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

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

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

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

$b + m = [2, 4]$

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

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

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

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

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

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) $b = [2,4]$

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

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

$b + m = [4, 3]$

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

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

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

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

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

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

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

$b + m = [1, 1]$

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

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

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

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

**earboth** · February 13th 2008, 11:17 PM

Originally Posted by Macleef

Let vector $m = [2, -1]$ and vector $b = [0, 6]$

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

...

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

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

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

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

**Macleef** · February 14th 2008, 11:29 AM

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

**earboth** · February 14th 2008, 11:44 AM

Originally Posted by Macleef

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

Then your results are OK.

The heads of all vectors form the line $y = -\frac12 x + 5$ or written as equation with vectors:

$(x, y) = (0, 5) + r \cdot (2, -1)$

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