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sp2606 [1]
3 years ago
10

Suppose B = {V1, ...,V6} is a set of six vectors in R4. (Note that no further information on the six vectors is provided.) Each

of the statements listed below contains three options: select the correct option and give evidence of your thinking. For example, if a statement is always true, you should explain why. If a statement may be true, you should provide examples.1. The vectors (do)(do not)(might not) span R4.2. The vectors (are) (are not)(may be) linearly independent. 3. Any four of these vectors (are)(are not)(may be) a basis for R4.
Mathematics
1 answer:
Aloiza [94]3 years ago
4 0

Answer:

Step-by-step explanation:

1) The vectors might no span R^4. if you want to span R^4, at least 4 vector of the six must be linear indepent. But, consider the following set of vectors

{(1,1,1,1), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)}. This set has 6 vectors of R4, but they are all linearly dependent, since they are a linear combination of the vector (1,1,1,1). Since we have only one linear indepent vector, we cannot span R4 with this set.

2) Since R4 is a 4-dimensional vector space, by having 6 vectors in an 4-dimensional space, the must necessarily be linearly dependent, since in R4 the maximum number of linearly independent vectors we could have in a set is 4.

3). The statement may be true. Any four subset of these vectors may be a base. To do so, that depends on their linear independence. If they are linearly independence, they are base since they are 4 linearly independent vectors in a 4-dimensional space, but if they lack linearly independence, they cannot be a base.

For example, consider the following set of vectors

{(1,0,0,0),(0,1,0,0),(0,0,1,0), (0,0,0,1), (1,1,1,1), (0,0,0,1)}.

Note that if we take the first 4 vectors, they are linearly indepent, hence they are a base. Same happens if we take vectors 2-5. But if we take vectors 3-6, then this subset is not a base, since it has only 3 linearly independent vectors.

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Marcus can read 126 pages in one hour. How many pages can he read in 15 minutes?
valina [46]

Answer:

31.5 or 32

Step-by-step explanation:

Divide 126 by 4

7 0
3 years ago
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Beginning from a depth of 35 ft below the surface, a whale swims upward and jumps to a height of nearly 17 feet above the surfac
Shtirlitz [24]

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6 0
3 years ago
1. How many ways are there to make an octagon with 19 different sticks when order DOESN’T matter?
mart [117]

Answer:

1. 19C8 = 75582

2. 19P8= 3047466240

Step-by-step explanation:

First, find the number of ways to get 8 sticks from 19. At first, you have 19 choices, then 18, then 17, all the way to 12. Giving you 19*18*17*...*13*12, or 19!/11!.

Combination:

When order doesn't matter, you have to divide 19!/11! by the number of ways to order 8 sides, or 19!/11!/8!=19C8=75582

Permutation:

When order doesn't matter, you don't have to divide 19!/11! by the number of ways to order 8 sides, since you count each of these, and 19!/11!=19P8=3047466240.

6 0
3 years ago
K +-23 = -100<br>help me
Alex_Xolod [135]

Answer:

-77

Step-by-step explanation:

-77 + -23 = -100

4 0
3 years ago
can some one help me with this iv been stuck for about a week and i need some help are these function why or why not? thanks!
FromTheMoon [43]

Answer:

1) f(x) is not a function

2) g(x) is  a function.

Step-by-step explanation:

Function is  defined as a relationship between the independent variable and  the dependent variable

If a variable y is so related to a variable x that whenever a numerical value is assigned to x, there is a rule according to which a unique value of y is determined, then y is said to be a function of the independent variable

The above function can be represented by y = f(x).  f(x) can also been represented g(x) and P(x) functions of the independent variable x,  when the   function is unknown or unspecified.

Two laws to become a function:

a) Every element in X is related to some element in Y.

This relationship is commonly symbolized as y = f(x). In addition to f(x), other abbreviated symbols such as g(x) and P(x) are often used to represent functions of the independent variable x, especially when the nature of the function is unknown or unspecified.

Two rules to become a function:

a)"Each element" means that every element in X is related to some element in Y.

But some elements of Y may not assigned to x

b) A function is assigned to a single value. It will not give back 2 or more elements for the same input.

One-to-many is unaccepted, while many-to-one is accepted

If the relationship does not satisfies those two rules then it is not a function. we can say that the given relationship not a function.

1) Let f(x) be the function

Given x is domain ie, x=\{-2-3\} and y=f(x) ie, y=\{2,3\} is the range of x

By the definition of function,  f(x) does not satisfies the rules  to be a function because f(-2)=2 and f(-2)=3 So it assigns two values.

Therefore  f(x) is not a function

2) Let g(x) be the function

x is domain ie, x=\{-2-1,0,1\} and y=g(x) ie, y=\{2,2.5,3,3.5\} is the range of x

By the definition function,  g(x)  satisfies the rules  to be a function because g(-2)=3 , g(-1)=3.5,g(0)=2 and g(1)=2 So it assigns exactly one value.

Therefore  g(x) is  a function.

3 0
3 years ago
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