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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:

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Step-by-step explanation:

we know that

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we have

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substitute

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antiseptic1488 [7]

Answer:

  • incorrect
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Step-by-step explanation:

A + B = (-4x^2 +2x -5) +(3x^2 +6) = x^2(-4+3) +x(2) +(-5+6) = -x^2 +2x +1

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Consider independent simple random samples that are taken to test the difference between the means of two populations. The varia
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Answer:

d. t distribution with df = 80

Step-by-step explanation:

Assuming this problem:

Consider independent simple random samples that are taken to test the difference between the means of two populations. The variances of the populations are unknown, but are assumed to be equal. The sample sizes of each population are n1 = 37 and n2 = 45. The appropriate distribution to use is the:

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Solution to the problem

When we have two independent samples from two normal distributions with equal variances we are assuming that  

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Where t follows a t distribution with n_1+n_2 -2 degrees of freedom and the pooled variance S^2_p is given by this formula:

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