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natka813 [3]
2 years ago
12

Suppose T: ℝ3→ℝ2 is a linear transformation. Let U and V be the vectors given below, and suppose that T(U) and T(V) are as given

. Find T(3U+2V).
U =

[1]

[2]

[1]

V =

[1]

[3]

[2]

T(U) =

[−2]

[5]

T(V) =

[−2]

[7]

T(3U+2V) = ?
Mathematics
1 answer:
ira [324]2 years ago
8 0

Answer:

T(3u+2v)=(-10,29)

Step-by-step explanation:

T is a linear transformation, hence it is homogeneous (T(cr)=cT(r) for all real c and r∈ℝ³) and additive (T(r+s)=T(r)+T(s), for all r,s∈ℝ³). Apply these properties with r=3u and s=2v to obtain:

T(3u+2v)=T(3u)+T(2v)=3T(u)+2T(v)=3(-2,5)+2(-2,7)=(-6,15)+(-4,14)=(-10,29)

We don't have an explicit definition of T, so it's more difficult to compute T(3u+2v) directly without using these properties.

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HDTV screens usually have a width-to -height ratio of 16:9. Which screen dimensions are in the same proportion?
love history [14]

Answer:

4 feet by 3 feet

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

Please have a look at the attached photo.  

My answer:

width-to -height ratio of 16:9

Let analyse all possible answers:

  • 4 feet by 3 feet

16 divided by 4 is the same as 9 divided by 3 => it is true

  • 28 inches by 21 inches

16 divided by 28 is different as 9 divided by 21 => it is wrong

  • 48 centimeters by 27 centimeters

16 divided by 48 is different as 9 divided by 27 => it is wrong

  • 26 inches by 19 inches

16 divided by 26 is different as 9 divided by 219=> it is wrong

We choose A.

Hope it will find you well.

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2 years ago
Casey likes to run she runs a additional 1/4 mile each day on the last day she ran 1 1/4 miles if she ran half a mile her first
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1/2 first day
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1 and 1/4=5/4
2/4+how many 1/4=5/4
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add 1 moe for the firs tday

3+1=4

4 days
3 0
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A coordinate plane with a point plotted at and labeled (0, 2).
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A,D, AND E

Step-by-step explanation:

4 0
2 years ago
One side of a rectangle is 3 feet shorter than twice the other side find the sides if the area is 209 feet squared
AfilCa [17]

Answer:

29119.66666...+14561.3333...=43681, 209ft^2, not square feet.

Step-by-step explanation:

<em>"One side of a rectangle is 3 feet shorter than twice the other side find the sides if the area is 209 feet squared"</em>

Ok, so this is a tricky one- <em> 209 feet squared, </em>not 209 square feet, therefore the area is 209^2, or 43,681.

Next, let's define our variables-

<em>x= the "other side"</em>

<em>z= 3 feet shorter than twice side</em>

We can now make these (useful) equations

z=2x-3

43681= (2x-3)+x

We will focus on the latter for now-

Simplify

43681= (2x-3)+x

43681= 2x-3+x

43681= 3x-3

+3

43684=3x

/3

14561.3333...=x

z=2x-3

z=2*(14561.3333)-3

z=29119.66666....

29119.66666...+14561.3333...=43681

6 0
2 years ago
A piece of string is 325 centimeters long. You need the string to be 114 meters long. How many centimeters should you cut off?
sertanlavr [38]

There are 100 centimeters in 1 meter.1 and 1/4 meters can also be written as 1.25, since 1/4 = 0.25.To find the answer, convert 1.25 meters to centimeters.
1 meter = 100 centimeters1.25 meters = x centimeters1.25 is 125% of 1. In other words, there is a 25% increase.
Now apply this increase to the centimeters side.125% = 1.251.25 • 100 = 125
So 1.25 meters (1 and 1/4 meters) equals 125 centimeters.
The string is 325 centimeters.In order for the string to be 125 centimeters, you need to cut some off.To find how much you need to cut off, subtract 125 from 325.325 - 125 = 200
Answer: In order for your string to be 1 and 1/4 meters, you must cut 200 centimeters off the original 325 centimeter long string.
5 0
2 years ago
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