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3 years ago

Need help asap pls :)a/3+a = ?a= -21

Mathematics

1 answer:

qaws [65]3 years ago

7 0

Answer: -28

Step-by-step explanation:

First, let's break it apart.

a/3 can be said as -21/3 -21/3 is -7

Then, you just add them.

-21+(-7)=-28

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Step-by-step explanation:

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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

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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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3 years ago

Please answer the question in the picture because it would paste correctly thanksss

o-na [289]

Answer:

Step-by-step explanation:

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3 years ago

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2. Explain how to calculate 8% of 350 by first calculating 1% of 350.

V125BC [204]

Answer:

Step-by-step explanation:

So 1% of 350 would be 3.5 because 350 divided by 100 is 3.5. You then get 3.5 and multiply it 8 times, which would be 28. (You multiply it 8 times because 8% is 8 times 1%.)

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2 years ago

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Need help asap pls :)a/3+a = ?a= -21​

Need help asap pls :)a/3+a = ?a= -21