Are extraneous solution always negative numbers
2 answers:
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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.
Answer:
You could use the polygon area formula OR here's an easier solution
We draw the lines DC and DE
Angle ADC = 120°
Triangle ADC is a 30 60 90 triangle
In such a triangle Line AE = hypotenuse * sq root (3) /2
Line AE = 3 * 0.8660254038 = 2.5980762114
Line DE = 1.5
Area of Triangle ADE = .5 * 1.5 * 2.5980762114 =
1.9485571586 square meters and entire area of Triangle
ABC = 6 * 1.9485571586
which equals 11.6913429513 square meters
Step-by-step explanation:
