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vampirchik [111]
2 years ago
14

Describe the translation of figure ABCD. Use the drop-down menus to explain your answer.

Mathematics
1 answer:
pickupchik [31]2 years ago
8 0

Answer:

Is Figure A'B'C'D' a translation of Figure ABCD? Explain. Yes; it is translated 2 units left and 2 units up.

Step-by-step explanation:

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* Let S = Span {(2,-1, 1), (3, 1, 1), (1, 2, 0)}. (i) Calculate the dimension of S.
Sholpan [36]

The span of 3 vectors can have dimension at most 3, so 9 is certainly not correct.

Check whether the 3 vectors are linearly independent. If they are not, then there is some choice of scalars c_1,c_2,c_3 (not all zero) such that

c_1 (2,-1,1) + c_2 (3,1,1) + c_3 (1,2,0) = (0,0,0)

which leads to the system of linear equations,

\begin{cases} 2c_1 + 3c_2 + c_3 = 0 \\ -c_1 + c_2 + 2c_3 = 0 \\ c_1 + c_2 = 0 \end{cases}

From the third equation, we have c_1=-c_2, and substituting this into the second equation gives

-c_1 + c_2 + 2c_3 = 2c_2 + 2c_3 = 0 \implies c_2 + c_3 = 0 \implies c_2 = -c_3

and in turn, c_1=c_3. Substituting these into the first equation gives

2c_1 + 3c_2 + c_3 = 2c_3 - 3c_3 + c_3 = 0 \implies 0=0

which tells us that any value of c_3 will work. If c_3 = t, then c_1=t and c_2 = -t. Therefore the 3 vectors are not linearly independent, so their span cannot have dimension 3.

Repeating the calculations above while taking only 2 of the given vectors at a time, we see that they are pairwise linearly independent, so the span of each pair has dimension 2. This means the span of all 3 vectors taken at once must be 2.

3 0
1 year ago
What is the GCF of 81, 252, and 567?
Leto [7]

It's 9. Take 81/9 and that equals nine

7 0
3 years ago
Help ASAP pls !!!!!!!!!!!!!
bonufazy [111]

Answer:

I think it's B.

Step-by-step explanation:

They are asking for integers greater than -3 and less than 5.

4 0
3 years ago
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velikii [3]

Answer:

.

Step-by-step explanation:

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3 years ago
Please answer, no jokes or fakes or report ​
Rama09 [41]

Answer:

375.2887 ft is the answer

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3 years ago
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