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:
15 pound in a bag
Step-by-step explanation:
one can= 8 oz
one bag= 30 times the amount in a can
8 oz x 30 = 240 oz in a bag
Question asked how many pound is in one bag of dog food:
We know that 16 oz = 1 pound
240 oz = x pound
To find x pound we divide 240 oz by 16 oz-->
240 oz/ 16 oz = 15 pound
Answer:
Hey there!
The trick to finding the value that completes the square, is dividing the middle number, the 10, by 2, and squaring that. Thus, we have 10/2=5, and 5^2=25.
c=25
Hope this helps :)
First you need to distribute the -8
So you would get -8x-8 now distribute the 3 so it would be 3x-6
-8x-8+3x-6=-3+2 is how it should look
Now combine the -8x and 3x cause their like terms and also -8 and -6
-5x-14=-3x+2 now add -3 to both sides
-2x-14=2 and add 14 to both sides
-2x=12 all left to do is divide both by -2
X=-6
Answer:
Niether of them are correct
Step-by-step explanation:
If you actually put into your calculator 2^28, it equals 268,435,456. This is because you're not just squaring 28, you are multiplying 2 by 2-- 38 times. This will quickly add up, even if you start out with 2 it will create a very large number.
