Answer:
Step-by-step explanation:
<u><em>the mean in period</em></u> 1 :
(2.3+2.1+2.2+2.2+2.2+2.1+2.4+2.5+2.2+2.0+1.9+1.9+2.1+2.2+2.3)÷15=21.733...
<u><em>the mean in period</em></u> 2 :
(2.3+2.1+3.3+1.5+3.6+1.6+3.0+1.1+4.7+2.1+2.4+1.9+2.8+0.5+2.3)÷15=23.466...
Since 23.466 > 21.733 then “The mean in period 2 is higher than the mean in period 1”.
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 =
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.