1. Is L = {1 − 2x + 3x^2, x − 2x^2, 2 − 5x + 8x^2} linearly independent? If yes, show why. If not, show a dependence relationship. Is L = {1 + 2x + 2x^2, x − 2x^2, −2 − 3x − 5x^2} linearly independent? If yes, show why. If not, show a dependence relationship.

Q: Express ax? + bx + c as a linear combination of the functions f(x) = 4, g(x) 2x, and h(x) = -x²,…

A: Sincewe can write every element of P2 in linear combination of f(x),g(x),h(x) so this functions…

Q: find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = x3 - 2x + 3, a = 2

A: We find f(x) and f'(x) at x=2

Q: Suppose , t2, ., , are linearly independent. Prove that S is linearly independent where (a) S=…

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Q: Show that ex and e−x are linearly independent in C(−∞,∞).

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Q: Find the linearization of ƒ(x, y) = x2 - xy + 1/2 y2 + 3 at the point (3, 2).

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Q: Is {x² – 2.x, x²+x, x²} linearly independent dependent? Prove your answer. or

A: Answer

Q: 5. Show how the origin changes stability as a changes by using the Poincaré Diagram. x - [i :]• 2 a…

A: The stability of fixed points of a system of constant coefficient linear differential equation of…

Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

Q: Identify whether the equation is partialor ordinany, linear or non inear and it order. ym = X

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Q: Show that the functions f, (x) = 4x" , and f2(x) = x"** are linearly independent on (-00, 00).

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Q: Distinguish between Linear and Nonlinear Relations

A: Linear Relation A relation can be said as a linear relation when there is two variable having degree…

Q: Find the linearization of ƒ(x) = 2/(1 - x) + √(1 + x) - 3.1 at x = 0.

A: Here The formula for the linearization is Here a = 0 Therefore,

Q: Suppose the clean water of a stream flows into Lake Alpha, then into Lake Beta, and then further…

A: Note: - According to our guideline i didn't solved more than three subparts . So please again repost…

Q: Find the linearization at x = a. f(x) = 6x®, a = 1

A: Linearization L(x) of function f(x) at a is given as L(x) = f(a) + f'(a)(x-a)

Q: The functions y1, Y2, . .. , Yn are linearly independent, if and only if W (y1, 32, ..., Yn)(to) #0…

A: If two functions are linearly dependent then the Wronskian is zero for every value of t.

Q: Use the Wronskian and any needed theorems to show that f1 = sin x + 2x2 and f2 = e3x are linearly…

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Q: Find a parameterization for a line passing through the points (1,1) and (5, 13) O x = t, y = 3t-2 O…

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Q: find the linearization at x = a. f (x) = x4, a = 1

A: Given function: Using the formula of linearization of a function f(x) at x =a :

Q: assume thatf (2, 3) = 8, fx (2, 3) = 5, fy (2, 3) = 7 Which of (a)–(b) is the linearization of f at…

A: Consider the given: f2,3=8fx2,3=5,fy2,3=7,

Q: Question * The set of functions {x + 1,x³ + x, 2x² – x – 3} - is linearly independent on the…

A: Linearly independent: Set of vectors x1, x2, x3....... is said to be linearly independent if  c1…

Q: Show f(x) = e2= and g(x) = x e²z linearly independent by finding its Wronskian.

A:

Q: 4-Find the coordinates the front trace F for line AB, if A(2, 1, -2) and B(3, 3, -5). * O (1,-1) O…

A: A=(2,1,-2) B=(3,3,-5)

Q: FInd the equation of a linw whose gradient is 3/2 and which passes through the point P,where P…

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Q: If ů, = |8|,02 = 5,03 show that {v1, v2, v3} is linearly dependent in R', and determine the linear…

A: Letv1=2i^+8j^+3k^v2=i^+5j^+2k^v3=i^+j^Let…

Q: х-у+2z (2,0, – 3) 2x + у-z'

A:

Q: Use the chain-rule and find x and y in terms of x, x, and if:

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Q: The functions y1, Y2, . .. , Yn are linearly independent, if and only if W (y1, Y2, ..., Yn)(to) # 0…

A: We can use the Wronskian test to check the functions are linearly independent or dependent.

Q: Use least-squares regression to fit a straight line y = f(x) = Ax+B  to:   xi -8 -3 0 4 6 yi 7 4 2…

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Q: Justify is it true or false? It is possible for variables to have r=0 but still have a strong…

A: If the relationship is linear between variables, then r = 0 means that there is no correlation…

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A: Decision Rule: If p-value ≤ α, then the variable is significant Let alpha=0.05. Term P value…

Q: By separating the variables convert the PDE into a system of ODES U = U x PLEASE HELP

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Q: Estimate the parameters a and b of best linear OLS equation for given points. ĵi = ax; + b 1 10 25…

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Q: Show that the functions y1= e^t,  y2 = e^-t, and te^-t are linearly independent.

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Q: A researcher collected data on ( X , Y ), and wanted to test if the true relationship is linear.…

A: To test whether true relationship is linear or not, consider Lack of fit F-test. H0: There is no…

Q: the set A = {2+x², 3+ 5x – 4x²} C P2(R) - -) Show that A is linearly independent.

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Q: Find the linearization of ƒ(x) = 2/(1 - x) + saqrt(1 + x) - 3.1 at x = 0

A: Given,

Q: Find and classify the stationary points of y= In 2x - 2x

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Q: Parameterize the following curve 9x 9x^2 + 4y^2 = 32y -54x-109

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Q: Which set of functions which is not linearly independent is  A-X^2,4x^3 B-2x,6x+3,3x+2 C-e^x,e^2x…

A: A set of functions will be linearly independent if there Wronskian is not equal to zero. Wronskian…

Q: The functions y1, Y2, · . . , Yn are linearly independent, if and only if W (y1, 22, *. Yn) (to) # 0…

A: Consider the following differential equation, y''+pxy'+qxy=0

Q: Find the value of x so that the following are linearly dependent in R³. (1, –1,0), (-1, x, 0), (0,2,…

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Q: Find the orthogonal trajectories of the family of lines 3x + 5y = C (A 3x - 5y = k (B 5x + Зу - k ©…

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Q: find the linearization at x = a. y = e√x , a = 1

A: Given function: Using the formula of linearization:

Q: Consider the linearizable functions as follows. Find new transformed variables (rª, yª, Bor B as you…

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Q: Show that {x, y} is linearly dependent if and only if x or y is a multiple of the other.

A: It is given that, x and y are two distinct non-zero vectors.

Q: Let fi = 1+x +x², f2 = 1+x +x*, f3 = 1 +x² + x°, ƒa = a +x +x² +x*. Determine a if if (f1, f2, f3;…

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Q: We called a nonlinear dif ferential equations if the dependent variables and their derivatives are…

A: We will look at the definition of non linear differential equations to answer this

Q: calculate x, , X2, Xg from the foloueng ノ equations using Gauss E limination method 一 3X, + X2 +…

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Q: Find a parameterization for a line passing through the points (0, 0) and (2, 8) O x=t, y = 4t Ox=t,…

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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.