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Ksju [112]
2 years ago
10

v={x,y,z} such that the points satisfies x-2y+3z=0. is v vector space? if not,find all for which v is not a victor space

Mathematics
1 answer:
atroni [7]2 years ago
5 0

Yes, the set of vectors

V = {(x, y, z) : x - 2y + 3z = 0}

is indeed a vector space.

Let u = (x, y, z) and v = (r, s, t) be any two vectors in V. Then

x - 2y + 3z = 0

and

r - 2s + 3t = 0

Their vector sum is

u + v = (x + r, y + s, z + t)

We need to show that u + v also belongs to V - in other words, V is closed under summation. This is a matter of showing that the coordinates of u + v satisfy the condition on all vectors of V:

(x + r) - 2 (y + s) + 3 (s + t) = (x - 2y + 3z) + (r - 2s + 3t) = 0 + 0 = 0

Then V is indeed closed under summation.

Scaling any vector v by a constant c gives

cv = (cx, cy, cz)

We also need to show that cv belongs to V - that V is closed under scalar multiplication. We have

cx - 2cy + 3cz = c (x - 2y + 3z) = 0c = 0

so V is need closed under scalar multiplication.

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2 years ago
Chris is behind in 9 classes of school he has a total time of 25 days to make up 75 hours and 4 minutes worth of late work how m
Vlad1618 [11]

Answer:

Step-by-step explanation:

First, convert the 4 mins into hours by dividing by 60;

4/60 =0.067

Add 0.067 to 75 hrs to get the total = 75+0.067 = 75.067

Therefore the total time Chris needs to make up for is 75.067 hrs

Total number of days Chris has = 25

Next,

IF in 25 days = he can cover 75.067hrs

then in 1 day he will cover = (1 * 75.067)/ 25

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Therefore, Chris needs to do 3hrs each day to be able to complete the deadline

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3 years ago
How do I solve this? (Geometry)
Luden [163]

Answer:

Step-by-step explanation:

(3×10×8)÷26400= 0.00909090909

hope it helps

8 0
2 years ago
Solve for x: 3/4x+5/8=4x
kompoz [17]
So, you have 3/4x + 5/8 = 4x. We can do this in two ways. Since fractions are harder to deal with, we can turn the fractions into whole numbers.

First we need to find the LCD (Least Common Denominator) between 4 and 8, which is 8. So multiply the 3/4x by 2/2, which gives you an equivalent fraction of 6/8x.

So now we have 6/8x + 5/8 = 4x. Now multiply both sides by 8, to get rid of the denominators of the fractions. That gives us 6x + 5 = 32x. Now use the subtraction property of equality to subtract 6x from both sides giving us 5 = 26x. 

Now you can use the division property of equality to divide 26 on both sides, which gives us x = 5/26.

Hope this helps. :D Feel free to ask any other questions, and if you have any questions about my explanation, don't hesitate to ask.
6 0
3 years ago
Round to the nearest hundredth : 3.2649
Bas_tet [7]

Answer:

3.26

Step-by-step explanation:

Rounding to the nearest hundredth means round to the nearest two decimal places.

To do this, all we need to look at is the 3rd decimal place.

Since 4 is not 5 or greater, that means we must round down, no matter how close it is to 5.

Therefore, the answer should just be 3.26

3 0
3 years ago
Read 2 more answers
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