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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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RESOLVER LOS SIGUIENTES SISTEMAS DE ECUACIONES APLICANDO EL METODO DE SUSTITUCION
kiruha [24]

Answer:

x = 1/2; y = 1/3

Step-by-step explanation:

2x + 3y = 2     Eq. 1

-6x + 12y = 1     Eq. 2

Eq. 1

2x + 3y = 2

2x = -3y + 2

x = -3/2 y + 1

Eq. 2

-6x + 12y = 1

De Eq. 1 sabemos que x = -3/2 y + 1

-6x + 12y = 1

-6(-3/2 y + 1) + 12y = 1

9y - 6 + 12y = 1

21y - 6 = 1

21y = 7

y = 7/21

y = 1/3

Eq. 1

2x + 3y = 2

2x + 3(1/3) = 2

2x + 1 = 2

2x = 1

x = 1/2

Respuesta: x = 1/2; y = 1/3

3 0
3 years ago
Sally was walking to Ocean Front Housing Complex, In miles, how far is her distance?
Vanyuwa [196]

Answer:

Sally is 10 miles

The coordinate ofthe deli is (1, -1)

Step-by-step explanation:

✍️Coordinate of Sally = (-3, 2)

Coordinate of Ocean Front = (5, -4)

The distance of Sally to Ocean Front Housing Complex = the distance between point (-3, 2) and (5, -4).

Use the distance formula, d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}, to calculate the distance between (-3, 2) and (5, -4):

d = \sqrt{(5 -(-3))^2 + (-4 - 2)^2}

d = \sqrt{(8)^2 + (-6)^2}

d = \sqrt{64 + 36}

d = \sqrt{100} = 10

✅The distance of Sally is 10 miles

✍️the coordinate of Deli would be half the distance between Sally and Ocean Front.

Therefore, use the midpoint formula to calculate the coordinate of the midpoint between Sally (-3, 2) and Ocean Front (5, -4).

Midpoint of (-3, 2) and (5, -4).

M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})

Plug in the values

M(\frac{-3 + 5}{2}, \frac{2 +(-4)}{2})

M(\frac{2}{2}, \frac{-2}{2})

M(1, -1)

✅The coordinate ofthe deli is (1, -1)

8 0
2 years ago
Answer ASAP PLEASE...
natka813 [3]

Answer:

Step-by-step explanation:

5 0
2 years ago
A certain right triangle has area 30 in. squared . one leg of the triangle measures 1 in. less than the hypotenuse. let x repres
Brut [27]
A) The length of the longer leg is x-1

b) Based on the area, the other leg is 2*30/(x -1). Based on the Pythagorean theorem, the other leg is √(x^2 -(x -1)^2).

c) Equating the two expressions for the shorter leg, we have
.. 60/(x -1) = √(2x -1)
.. 3600/(x -1)^2 = (2x -1)
.. (2x -1)(x^2 -2x +1) = 3600
.. 2x^3 -5x^2 +4x -3601 = 0

d) There is one positive real root, at x=13. A graphical solution works well.

The three sides of the triangle are 5 in, 12 in, 13 in.


_____
5-12-13 is a well-known Pythagorean triple. It is the next smallest one after 3-4-5.

6 0
3 years ago
A) 5x – 6y = 25 [x, y = 10]​
lora16 [44]
Ok so what u want to 58
3 0
2 years ago
Read 2 more answers
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