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maksim [4K]
3 years ago
12

3. Let U and V be subspaces of a vector space W. Prove that their intersection UnV is also a subspace of W

Mathematics
1 answer:
kenny6666 [7]3 years ago
7 0

Answer:  The proof is done below.

Step-by-step explanation:  Given that U and V are subspaces of a vector space W.

We are to prove that the intersection U ∩ V is also a subspace of W.

(a) Since U and V are subspaces of the vector space W, so we must have

0 ∈ U and 0 ∈ V.

Then, 0 ∈ U ∩ V.

That is, zero vector is in the intersection of U and V.

(b) Now, let x, y ∈ U ∩ V.

This implies that x ∈ U, x ∈ V, y ∈ U and y ∈ V.

Since U and V are subspaces of U and V, so we get

x + y ∈ U  and  x + y ∈ V.

This implies that x + y ∈ U ∩ V.

(c) Also, for a ∈ R (a real number), we have

ax ∈ U and ax ∈ V (since U and V are subspaces of W).

So, ax ∈ U∩ V.

Therefore, 0 ∈ U ∩ V and for x, y ∈ U ∩ V, a ∈ R, we have

x + y and ax ∈ U ∩ V.

Thus, U ∩ V is also a subspace of W.

Hence proved.

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Answer:

12 ; 12 dollars

Step-by-step explanation:

Data provided in the question:

Revenue function, R = 12x

R is in dollars

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or

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R = 12 × 1 = 12 dollars

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3 years ago
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antiseptic1488 [7]
Hey their,

3/4 
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How i got this was 36/12=3
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7 0
3 years ago
Round off 787592799 to the nearest 10​
timama [110]

Answer:

787592800

Step-by-step explanation:

Hi there,

If you round this answer to the nearest tens place, it would be 787592800. Since the 799 is closer to 800 rather than 790, it would round up and change the last three digits of the number instead of the usual two digits.

Hope this answer helps. Cheers.

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Step-by-step explanation:

When two line is perpendicular to each other the product of them is - 1

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