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3 years ago

Determine whether the following statements are True or False.

Mathematics

1 answer:

Stella [2.4K]3 years ago

6 0

Answer:

1) False

2) False

3) True

4) False

Step-by-step explanation:

1) Flase, {v1,v2,v3, ..., vp} is a base for H when they span H and also they are linearly independent.

2) False. A single nonzero vector is linearly independent , not dependent. There is not null linear combination that gives 0 as a result involving that vector.

3) True, if the columns werent linearly independent, we could triangulate the matrix and obtain 0, so the matrix wouldnt be invertible. This means that the columns should be linearly independent for the matrix to be invertible and as a consecuence, they will spam a subspace of R^n of dimension n, which means that they will spam all R^n and therefore, they form a basis of R^n.

4) False. A basis is a spanning set that is as small as possible. Larger spanning sets will have extra elements apart from those who can form a base toguether. Those elements will make the set linearly dependent.

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Answer:

$\huge \red{ c_3 = - 1}$

Step-by-step explanation:

$c_1 = 1 \\ \\ c_n= - 2c_{n-1}+5 \\ \\ c_2 = - 2c_{2-1}+5 \\ \\ c_2 = - 2c_{1}+5 \\ \\ c_2 = - 2(1)+5 \\ \\ c_2 = - 2+5 \\ \\ \huge \purple{c_2 =3} \\ \\ c_3 = - 2c_{3-1}+5 \\ \\ c_3 = - 2c_{2}+5 \\ \\ c_3 = - 2(3)+5 \\ \\ c_3= - 6+5 \\ \\ \huge \red{ c_3 = - 1}$

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3 years ago

Which expression is equivalent to 3^8 times 3^7?

m_a_m_a [10]

Answer:

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2 years ago

PLEASE!!!!! HELP ME!!!!!!

kati45 [8]

Answer:

$15 = a_1 r^4$ (1)

$1 = a_1 r^5$ (2)

If we divide equations (2) and (1) we got:

$\frac{r^5}{r^4}= \frac{1}{15}$

And then $r= \frac{1}{15}$

And then we can find the value $a_1$ and we got from equation (1)

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And then the general term for the sequence would be given by:

$a_n = 759375 (\frac{1}{15})^n-1 , n=1,2,3,4,...$

And the best option would be:

C) a1=759,375; an=an−1⋅(1/15)

Step-by-step explanation:

the general formula for a geometric sequence is given by:

$a_n = a_1 r^{n-1}$

For this case we know that $a_5 = 15, a_6 = 1$

Then we have the following conditions:

$15 = a_1 r^4$ (1)

$1 = a_1 r^5$ (2)

If we divide equations (2) and (1) we got:

$\frac{r^5}{r^4}= \frac{1}{15}$

And then $r= \frac{1}{15}$

And then we can find the value $a_1$ and we got from equation (1)

$a_1 = \frac{15}{r^4} = \frac{15}{(\frac{1}{15})^4} =759375$

And then the general term for the sequence would be given by:

$a_n = 759375 (\frac{1}{15})^n-1 , n=1,2,3,4,...$

And the best option would be:

C) a1=759,375; an=an−1⋅(1/15)

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Given:

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To determine the total distance (in mile) that Gregory ran, we refer to the given percentage:

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The total distance that Gregory ran is 2 miles. <span />

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3 years ago