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3 years ago

Find the sum of the arithmetic sequence. -10, -7, -4, -1, 2, 5, 8

Mathematics

1 answer:

Vadim26 [7]3 years ago

4 0

The arithmetic sequence is +3 for every number you move to the right.

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Can someone check my answers for my homework im not sure i did it right

zalisa [80]

Answer:

i think you did it right :)

Step-by-step explanation:

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3 years ago

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madreJ [45]

Answer is 15

A=1/2 bh
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3 years ago

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:

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4 years ago

If I have 12 apples and I give 11 to Chyanna how many do I have left to give away ??

bonufazy [111]

You have 1 left.
12-11= 1
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3 years ago

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What is this please help I'll give you a brainliest

scZoUnD [109]

(4,0) i think, it only makes sense since its a square

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