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]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%261%260%5C%5C7%260%261%5C%5C7%26-1%261%5Cend%7Barray%7D%5Cright%5D)
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.
Answer:
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Answer:
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Step-by-step explanation:
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Given:
7 red candies
9 blue candies
12 pink candies
Condition:
Number of bags that has equal number of candies.
We can do 7 bags with 1 colored candy each. There will be an excess of 2 blue candies and 5 pink candies.
We can do 4 bags with 1 red candy, 2 blue candies, 3 pink candies. There will be an excess of 3 red candies and 1 blue candy.
We can do 3 bags with 2 red candies, 3 blue candies, 4 pink candies. There will be an excess of 1 red candy.
Slope = raise / run
(211.1 - 212.0) / (0.5-0) = - 1.8
(210.2 - 211.1) / (1.0-0.5) = - 1.8
(208.4 - 210.2) / (2.0 - 1.0) = - 1.8
You can check, the other points. The slope is constant because the function is a linear equation,
Answer: - 1.8
