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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.

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Step-by-step explanation:

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8 0
2 years ago
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B = 2c + 6 what is the function?
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Answer:

2c put me as brainlest

Step-by-step explanation:

Let's solve for c.

b=2c+6

Step 1: Flip the equation.

2c+6=b

Step 2: Add -6 to both sides.

2c+6+−6=b+−6

2c=b−6

Step 3: Divide both sides by 2.

2c

2

=

b−6

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1

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Answer:

c=

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b−3

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