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ioda
2 years ago
10

Test the set of polynomials for linear independence. If it is linearly dependent, express one of the polynomials as a linear com

bination of the others. (If the set is linearly independent, enter INDEPENDENT. If the set is linearly dependent, enter your answer as an equation using the variables f, g, h, and j as they relate to the question.)
{f(x) =7 + x, g(x) = 7 +x^2, h(x)=7 - x + x^2} in P^2
Mathematics
1 answer:
aliina [53]2 years ago
5 0

Answer:

The set of polynomial  is Linearly Independent.

Step-by-step explanation:

Given - {f(x) =7 + x, g(x) = 7 +x^2, h(x)=7 - x + x^2} in P^2

To find - Test the set of polynomials for linear independence.

Definition used -

A set of n vectors of length n is linearly independent if the matrix with these vectors as columns has a non-zero determinant.

The set is dependent if the determinant is zero.

Solution -

Given that,

f(x) =7 + x,

g(x) = 7 +x^2,

h(x)=7 - x + x^2

Now,

We can also write them as

f(x) = 7 + 1.x + 0.x²

g(x) = 7 + 0.x + 1.x²

h(x) = 7 - 1.x + 1.x²

Now,

The coefficient matrix becomes

A = \left[\begin{array}{ccc}7&1&0\\7&0&1\\7&-1&1\end{array}\right]

Now,

Det(A) = 7(0 + 1) - 1(7 - 7) + 0

           = 7(1) - 1(0)

           = 7 - 0 = 7

⇒Det(A) = 7 ≠ 0

As the determinant is non- zero ,

So, The set of polynomial  is Linearly Independent.

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Answer:

after 6 months

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12 + 20(6) = 132

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3 years ago
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5 0
3 years ago
Help me;( i dont understand
PilotLPTM [1.2K]

Given:

Line l and line m are parallel.

Co-interior angles are (12x - 8)° and 104°.

To find:

The value of x.

Solution:

Sum of co-interior angles = 180°

12x° - 8° + 104° = 180°

12x° + 96° = 180°

Subtract 96° from both sides.

12x° + 96° - 96° = 180° - 96°

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7 0
3 years ago
The population of mastertown was 23,000 in 2012. assume that mastertowns population increases at a rate of 2% per year. write an
Svetlanka [38]
Alright, let's interpret it, first.

The question is asking us to first find two percent of 23,000, then right an equation.

Alright, first, let's find two percent of 23,000. To find that we must do 0.02*23,000

I got 460

So we know that Mastertown's population is increasing by 460 people per year. All we have to do now is plug that into the equation.

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4 0
3 years ago
Need a little help!
zhenek [66]
Answer = 7234.6 cm cu.
Reason
Volume of sphere
V= 4/3 x TT x r^3
V = 4/3 x 3.14 x 12^3
V= 7234.56
Rounded to 7234.6
5 0
2 years ago
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