Answer: (1,-2), (1, 3)
Step-by-step explanation:y=2x+1
Y=2(1)+1
Y=2+1
Y=3
3=2x+1
-1 -1
2=2x
_ _
2 2
X= 1 new you got your perpendicular line
So answer is (1, -2), (1, 3)
Known :
Ratio = Greg : Harry = 1 : 3
Greg's money = £8
Asked :
Harry's money = ...?
Answer :
![\: \ \: \: \: \: \: \: \frac{1}{3} = \frac{greg}{harry} \\ \: \: \: \: \: \: \: \: \frac{1}{3} = \frac{8}{harry} \\ harry = \frac{3 \times 8}{1} \\ harry = 24](https://tex.z-dn.net/?f=%20%5C%3A%20%20%5C%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7Bgreg%7D%7Bharry%7D%20%20%5C%5C%20%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7B8%7D%7Bharry%7D%20%20%5C%5C%20harry%20%3D%20%20%5Cfrac%7B3%20%5Ctimes%208%7D%7B1%7D%20%20%5C%5C%20harry%20%3D%2024)
So, Harry gets £24
<em>Hope </em><em>it </em><em>helpful </em><em>and </em><em>useful </em><em>:</em><em>)</em>
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.
I uploaded the answer to a file hosting. Here's link:
tinyurl.com/wtjfavyw