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:
Since 4 is the largest number its the hypotenuse. The two 3s are equal so they are interchangeable so it doesn't matter where you put them. If its a right triangle the hypotenuse is opposite the right angle.
Step-by-step explanation:
Answer:
1) 102.7 meters
2) 11
Step-by-step explanation:
1) -4.9x² + 75x = -4.9x² + 50x + 38
25x = 38
x = 1.52 s
Height = -4.9(1.52)² + 75(1.52) = 102.67904 m = 102.7 m
2) f(x) = x² + 3x - 2
f(2) = 2² + 3(2) - 2 = 8
f(6) = 6² + 3(6) - 2 = 52
Average rate of change:
(52-8)/(6-2) = 11
Answer:
8.81 KG (8810 g)
Step-by-step explanation:
8.1 KG (8100 g) + 710 g
Step-by-step explanation:
sorry..by any chance if my answer is incorrect