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.
We can use the Sine Law:a / sin A = b / sin B2 / sin 75° = 3 / sin B2 / 0.966 = 3 / sin B ( after that we will cross multiply )
2 sin B = 3 · 0.9662 sin B = 2.898sin B = 2.898 : 2sin B = 1.499 > 1 ( it is not possible )Answer: A ) No triangles can be formed.
Answer:
5/8
Step-by-step explanation:
1/4 (2/2)=2/8
3/8 (already simplified)
2/8+3/8=5/8
Answer:
This is your answer.
Step-by-step explanation:
There are different kinds of angles:
Angles below 90= Acute
90= Right
91–179= Obtuse
180= Straight Angle
181–359= Reflex Angle
360= Complete Angle or Circle.
Because 80 degrees is less than 90 degrees, Angle ABC is an acute angle.
Answer:
0.220 L
Step-by-step explanation:
One liter is 1000 mL, so 2,220 mL is 2.220 L. Subtracting the 2 L on hand gives the additional amount required:
2.220 L - 2 L = 0.220 L
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The nice thing about metric units is that conversion factors are often powers of 10, so only movement of the decimal point is required. It can be worthwhile to become familiar with the SI prefixes.