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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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50% of what number is 11.72
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Answer:

50% of what number is 11.72 = 23.44

Step-by-step explanation:

50% is half, so simply doube it.

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3 years ago
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3 0
3 years ago
Use the figure below to answer the following questions.
yan [13]

Answer:

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Step-by-step explanation:

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hope it's correct

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3 years ago
Find the largest integer which belongs to the following interval: (−∞; 31]
Studentka2010 [4]

Answer:

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Step-by-step explanation:

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The find the largest integer that belongs to the interval (-∞, 31] the numbers are arranged on the number line as follows

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8 0
3 years ago
Evaluate each expression.<br> 6! =<br> 3!. 21 =<br> 11
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Answer:

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N! = N*(N-1)*.....*2*1

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8 0
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