If a case of 24 cans of peaches costs $7.50 how much does each can cost to the nearest cent

L :V --> W is a linear transformation. Prove each of the following (a) ker L is a subspace of V. (b) range L is a subspace of

iragen [17]

Answer:

a) Assume that $x,y\in\ker L$ , and $\alpha$ is a scalar (a real or complex number).

First. Let us prove that $\ker L$ is not empty. This is easy because $L(0_V)=0_W$ , by linearity. Here, $0_V$ stands for the zero vector of V, and $0_W$ stands for the zero vector of W.

Second. Let us prove that $\alpha x\in\ker L$ . By linearity

$L(\alpha x) = \alpha L(x)=\alpha 0_W=0_W$ .

Then, $\alpha x\in\ker L$ .

Third. Let us prove that $y+ x\in\ker L$ . Again, by linearity

$L(x+y)=L(x)+L(y) = 0_W + 0_W=0_W$ .

And the statement readily follows.

b) Assume that $u$ and $v$ are in range of $L$ . Then, there exist $x,y\in V$ such that $L(x)=u$ and $L(y)=v$ .

First. Let us prove that range of $L$ is not empty. This is easy because $L(0_V)=0_W$ , by linearity.

Second. Let us prove that $\alpha u$ is on the range of $L$ .

$\alpha u = \alpha L(x) = L(\alpha x) = L(z)$ .

Then, there exist an element $z\in V$ such that $L(z)=\alpha u$ . Thus $\alpha u$ is in the range of $L$ .

Third. Let us prove that $u+v$ is in the range of $L$ .

$u+v = L(x)+L(y) = L(x+y)=L(z)$ .

Then, there exist an element $z\in V$ such that $L(z)= u +v$ . Thus $u +v$ is in the range of $L$ .

Notice that in this second part of the problem we used the linearity in the reverse order, compared with the first part of the exercise.

Step-by-step explanation:

6 0

3 years ago

What is 7/8 - 2/3 in fractions?

Mademuasel [1]

Answer: 5/24

Step-by-step explanation:

7/8 = 21/24 2/3= 16/24

21/24 - 16/24 = 5/24

5 0

3 years ago

28/a + 6 = Plss I need help

dedylja [7]

Answer:

$\frac{28 + 6a}{a}$

Step-by-step explanation:

6 0

3 years ago

You have a 4 in. X 6in. family picture that you want to resize. You can choose from a 16 in. X 20 in. or an 18 in. X 24 in. Whic

mixas84 [53]

Answer:

1.333 is more close to 1.5 than 1.25 .

Step-by-step explanation:

We are given:

You have a 4 in. X 6in. family picture that you want to resize. You can choose from a 16 in. X 20 in. or an 18 in. X 24 in. Which size will keep more of the original picture.

First divide 6 by 4: we get,

6/4 = 1.5 inches

This is the ratio to achieve.

Now divide 20 by 16

20/16 = 10/8

10/8 = 5/4

5/4 = 1.25 inches

Now divide 24 by 18

24/18 = 12/9

12/9 = 4/3

4/3 = 1.333 inches

1.333 is more close to 1.5 than 1.25 .

7 0

3 years ago

Read 2 more answers

Mr Newman bought a ticket to a chili supper and spend a total of $30 he bought a combination of adult tickets for $3 each which

Debora [2.8K]

Answer:

60

Step-by-step explanation:

To make 60 all you need to do is 30*3=60 I believe that it is 60

8 0

3 years ago