Directions: 1. At any time, you may reset the applet by pressing the refresh symbol in the top right. You can zoom out the applet by using your scroll wheel on your mouse inside the applet. You can drag inside the applet to see more to each side as well. 2. Do the given task below and answer the given questions using the REPLY button Task 1: You must use the given vectors 1 and 2. The only things that you can adjust are the weights C1 and 2 by moving the sliders left and right. Questions (a) What weights can we choose so that c₁*₁ + C22 is the zero vector? (b) Are your weights from (a) unique, or are there other choices? If there are other choices, what is another choice? Task 2: Now you may choose your own vectors 1 and 2 by sliding the blue and green vertices, respectively. You can also still adjust the weights C1 and 2 by moving the sliders left and right. Questions (c) Give an example of a linear combination that resulted in the zero vector that did NOT have O's for the weights. (d) What is interesting about your vectors 1 and 2 from (c)? C ₁ =2 10 C₁1+ C₂#₂ = C₁₂=3 ₁ = (1) #₂ = (²) -20 -18, -16 ₁2 = 0₁²₂= 3 (7) = (3) -14 C11 -10 -8 -6 -4 12²1 +₂²₂ c₂t₂ 6 10
Directions: 1. At any time, you may reset the applet by pressing the refresh symbol in the top right. You can zoom out the applet by using your scroll wheel on your mouse inside the applet. You can drag inside the applet to see more to each side as well. 2. Do the given task below and answer the given questions using the REPLY button Task 1: You must use the given vectors 1 and 2. The only things that you can adjust are the weights C1 and 2 by moving the sliders left and right. Questions (a) What weights can we choose so that c₁*₁ + C22 is the zero vector? (b) Are your weights from (a) unique, or are there other choices? If there are other choices, what is another choice? Task 2: Now you may choose your own vectors 1 and 2 by sliding the blue and green vertices, respectively. You can also still adjust the weights C1 and 2 by moving the sliders left and right. Questions (c) Give an example of a linear combination that resulted in the zero vector that did NOT have O's for the weights. (d) What is interesting about your vectors 1 and 2 from (c)? C ₁ =2 10 C₁1+ C₂#₂ = C₁₂=3 ₁ = (1) #₂ = (²) -20 -18, -16 ₁2 = 0₁²₂= 3 (7) = (3) -14 C11 -10 -8 -6 -4 12²1 +₂²₂ c₂t₂ 6 10
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Transcribed Image Text:Directions:
1. At any time, you may reset the
applet by pressing the refresh
symbol in the top right. You
can zoom out the applet by
using your scroll wheel on
your mouse inside the applet.
You can drag inside the applet
to see more to each side as
well.
2. Do the given task below and
answer the given questions
using the REPLY button
Task 1: You must use the given
vectors 1 and 2. The only things
that you can adjust are the
weights C1 and C2 by moving the
sliders left and right.
Questions
(a) What weights can we choose
so that C₁1 C22 is the zero
vector?
(b) Are your weights from (a)
unique, or are there other
choices? If there are other
choices, what is another choice?
Task 2: Now you may choose your
own vectors 1 and 2 by sliding
the blue and green vertices,
respectively. You can also still
adjust the weights C1 and 2 by
moving the sliders left and right.
Questions
(c) Give an example of a linear
combination that resulted in the
zero vector that did NOT have O's
for the weights.
(d) What is interesting about your
vectors 1 and 2 from (c)?
C
C₁ = 2
10
C₂ = 3 C₁₁+ C₂₂ =
(3)
-14 -12 -10 -8
(3)
-20 -18 -16
C₁1 2
C₂2= 3 =
#₂ =
C171
-6 -4
-2
0
-6
-8
2
0₁51+0₂5²₂
C₂t2
8
4
6
10
G
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