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:
0.43
Step-by-step explanation:
2+3+1+1=7
7*4+28==Area of full shape
(2*4)+(1*4)=12==Area of shaded shapes
12/28=0.428571>rounded up>0.43
Answer:
8 years
Step-by-step explanation:
Compound interest formula

A(t) is the final amount 55000
A_0= 40000, r= 4% = 0.04, for quarterly n=4

divide both sides by 40000


Take ln on both sides

divide both sides by ln(1.01)

Divide both sides by 4
t=8.00108
So it takes 8 years
Answer:
(3,10)
Step-by-step explanation:
When x is 3

y is 11, and this is invalid because it is not at accord.