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xenn [34]
3 years ago
8

Please answer truefully i giv you brainlistet

Mathematics
1 answer:
jasenka [17]3 years ago
5 0
First: negative 9 and the second is 3 and 9
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Consider the linear transformation T from V = P2 to W = P2 given by T(a0 + a1t + a2t2) = (2a0 + 3a1 + 3a2) + (6a0 + 4a1 + 4a2)t
Svet_ta [14]

Answer:

[T]EE=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]

Step-by-step explanation:

First we start by finding the dimension of the matrix [T]EE

The dimension is : Dim (W) x Dim (V) = 3 x 3

Because the dimension of P2 is the number of vectors in any basis of P2 and that number is 3

Then, we are looking for a 3 x 3 matrix.

To find [T]EE we must transform the vectors of the basis E and then that result express it in terms of basis E using coordinates and putting them into columns. The order in which we transform the vectors of basis E is very important.

The first vector of basis E is e1(t) = 1

We calculate T[e1(t)] = T(1)

In the equation : 1 = a0

T(1)=(2.1+3.0+3.0)+(6.1+4.0+4.0)t+(-2.1+3.0+4.0)t^{2}=2+6t-2t^{2}

[T(e1)]E=\left[\begin{array}{c}2&6&-2\\\end{array}\right]

And that is the first column of [T]EE

The second vector of basis E is e2(t) = t

We calculate T[e2(t)] = T(t)

in the equation : 1 = a1

T(t)=(2.0+3.1+3.0)+(6.0+4.1+4.0)t+(-2.0+3.1+4.0)t^{2}=3+4t+3t^{2}

[T(e2)]E=\left[\begin{array}{c}3&4&3\\\end{array}\right]

Finally, the third vector of basis E is e3(t)=t^{2}

T[e3(t)]=T(t^{2})

in the equation : a2 = 1

T(t^{2})=(2.0+3.0+3.1)+(6.0+4.0+4.1)t+(-2.0+3.0+4.1)t^{2}=3+4t+4t^{2}

Then

[T(t^{2})]E=\left[\begin{array}{c}3&4&4\\\end{array}\right]

And that is the third column of [T]EE

Let's write our matrix

[T]EE=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]

T(X) = AX

Where T(X) is to apply the transformation T to a vector of P2,A is the matrix [T]EE and X is the vector of coordinates in basis E of a vector from P2

For example, if X is the vector of coordinates from e1(t) = 1

X=\left[\begin{array}{c}1&0&0\\\end{array}\right]

AX=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]\left[\begin{array}{c}1&0&0\\\end{array}\right]=\left[\begin{array}{c}2&6&-2\\\end{array}\right]

Applying the coordinates 2,6 and -2 to the basis E we obtain

2+6t-2t^{2}

That was the original result of T[e1(t)]

8 0
3 years ago
A water container holds 2 liters. How many
EastWind [94]

Number of containers for 2 litres of water = 1

So, number of containers for 1 litre of water = ½

So, number of containers for 30 litres of water

= ½ × 30

= 30/2

= 15

So, 15 of these containers would be needed to fill a 30-liter drum.

5 0
3 years ago
Read 2 more answers
What is the slope of a line parallel to the line whose equation is
Lyrx [107]

Answer:

slope = 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

9x - 3y = - 54 ( subtract 9x from both sides )

- 3y = - 9x - 54 ( divide all terms by 0 3 )

y = 3x + 18 ← in slope- intercept form

with slope m = 3

Parallel lines have equal slopes, thus

slope of parallel line is 3

8 0
2 years ago
Answer the question below.
gregori [183]

Answer:

1/3

Step-by-step explanation:

4 0
3 years ago
Which property of multiplication is shown?<br><br> 9 × 0 − 6 × 0 = (9 − 6) × 0
JulsSmile [24]

Answer: Associative property

Step-by-step explanation: it is the same equation but they switched the numbers around on the other side of the equal sign so therefore its associative property

7 0
3 years ago
Read 2 more answers
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