1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
NikAS [45]
3 years ago
6

Let T: Mmxn(R)Mmxn(R) be the function defined

Mathematics
1 answer:
alexandr402 [8]3 years ago
5 0

Answer:

True. See the explanation and proof below.

Step-by-step explanation:

For this case we need to remeber the definition of linear transformation.

Let A and B be vector spaces with same scalars. A map defined as T: A >B is called a linear transformation from A to B if satisfy these two conditions:

1) T(x+y) = T(x) + T(y)

2) T(cv) = cT(v)

For all vectors x,y \in V and for all scalars c \in R. And A is called the domain and B the codomain of T.

Proof

For this case the tranformation proposed is t: M_{mxn} (R) > M_{nxm} (R)

Where T(A) = A^T

For this case we have the following assumption:

1) The transpose of an nxm matrix is an nxm matrix

And the following conditions:

2) T(A+B) = (A+B)^T = A^T + B^T = T(A) + T(B)

And we can express like this T(A+B) =T(A) + T(B)

3) If A \in M_{mxn}(R) and c \in R then we have this:

T(cA) = (cA)^T = cA^T = cT(A)

And since we have all the conditions satisfied, we can conclude that T is a linear transformation on this case.

You might be interested in
I'm having g a hard time with this, anyone please care to solve it for me? I would highly appreciate it.​
Damm [24]

Answer:

43 46 34 98 78 67

Step-by-step explanation:

8 0
3 years ago
Susan drove at an average speed of 30 miles per hour for the first 30 miles of a trip and then at an average speed of 60 miles p
garik1379 [7]
The average speed is given by:
average speed=(total distance)/(total time)
total time for the first 30 miles was:
time=distance/speed
=30/30
=1 hr
total time for the remaining 30 miles
=30/60
=0.5
hence the average speed will be:
speed=(30+30)/(1+0.5)=60/1.5=40 miles per hour 
8 0
3 years ago
Find the distance between (3,4) and (4,-6) if necessary, round to the nearest tenth.
Ratling [72]

Answer:

The distance is:

d = 10.0 units (Rounded to the nearest the Tenths Place)

Step-by-step explanation:

Given the points

  • (3,4)
  • (4,-6)

The distance 'd' between (3,4) and (4,-6)

\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):

d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}

substituting the points values

   =\sqrt{\left(4-3\right)^2+\left(-6-4\right)^2}

   =\sqrt{1+10^2}

   =\sqrt{1+100}

   =\sqrt{101}

   =10.0  units (Rounded to the nearest the Tenths Place)

Thus, the distance is:

d = 10.0 units (Rounded to the nearest the Tenths Place)

4 0
3 years ago
Every 8 hours, a company is able to manufacture 14 tents. Suppose that the total number of tents, y, is graphed agains the total
dolphi86 [110]
Evey 8 hours is the answer hope this helps
5 0
3 years ago
Please help someone anyone please help
Brrunno [24]

Answer:

if 135 calories represents 1/4 then a whole cup is 540 calories so two cups is 540 times 2 which is 1080

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • 3/4 = what number over 20? Trying to find the Equivalent Fraction
    9·2 answers
  • 4 5/8 - 2 11/20 = <br> What is the answer
    10·2 answers
  • Side B C is 10 inches long, and Side A B is StartRoot 300 EndRoot inches long. What is the length of Side A C?
    5·2 answers
  • . Fast train gets from the starting to the final station in 4 hours and 20 minutes. The slower local train, whose average speed
    15·1 answer
  • What is the equation of a line, in a slope-intercept form, that goes through the point (-12,7) with m= -(5/3)
    5·1 answer
  • Write the equation of the line parallel to the line 3x + 5y = 7 and passes through the point (-1, 3) in standard form. Please he
    14·1 answer
  • Find the vertex of the parabola y = 2x2 + 10x + 8
    6·1 answer
  • The data represented by the following stem-and-leaf plot range from to 2|578 3|24 4|129 5|03 A. 28 50 C. 25, 50 O 25 53
    5·1 answer
  • What is the measure of angle 2​
    7·2 answers
  • Match each equation on the left with its simplified version from the choices on the right. Do not solve. (not all the choices wi
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!