The functions y1, Y2, . .. , Yn are linearly independent, if and only if W (y1, Y2, ..., Yn)(to) # 0 for some to - True False

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: Let z = ƒ(u, y), u = ax + by, and y = ax - by. Express zx andzy in terms of fu , fy , and the…

A: Given, Let z=f(u,Y) u=ax+byY=ax-by

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

A:

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = √(x2 + y2 +…

A: Given: Function f(x,y,z) as follows: and a point (1,2,2) To find: Linearization L(x,y,z) of the…

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

A:

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

A: Answer

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

A:

Q: Show that the set {1, x, x2, ... , xn} is linearly independent in Pn(F).

A: Given, {1, x, x2, ... , xn}

Q: Determine: If S = {X2,1 + X2} is linearly independent or dependent.

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: Find the linearization of f(r, y, z) = x + y² + z³ at the point (1, 2, -1).

A:

Q: The set of functions {Vx, x, x²} is linearly dependent on (0, oo). True False

A:

Q: [2] Show that the functions f (x) = 4x" , and f,(x) = x*+* linearly independent (-00, 00). are on

A: To Show: Show that the functions f1x = 4xn, and f2x = xn+4 are linearly independent on -∞, ∞…

Q: 2 Given t = -1 and U = -1|, for which is the set {u, T, w} {d, v, 2 linearly independent?

A: Given that, u→=1-12 and v→=2-11 We have to find the vector w→ for which the set u→, v→, w→ is…

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: Q1) Use a suitable Linearization to find the best fit of the form f(x) = Cx3 + for the %3D data:…

A: Given the data,                 (1, -1), (2, 7), (3, 26.3)

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = x2 + y2 + z2…

A: given that a function f(x,y,z)=x2+y2+z2 we need to find the linearizations of f(x,y,z) at (1,1,1).…

Q: The functions y1, 2, ..., Yn are linearly independent, if and only if W (91, 32, ..., Yn)(to) #0 for…

A:

Q: = In z are two linearly indepen- of ry" + y' = 0, then the partic- - ry" + y' = f(x) can be written…

A: We have to choose the correct answer from the given options according to the given condition

Q: If S and T are normal linear operators satisfying ST* = T* S and TS* = S*T, show that their sum S+T…

A: I have used just definition of normal operator

Q: Show that the functions e^x , e^2x , e^3x are linearly independent.

A:

Q: Please solve this linear algebra question for me.

A: We are given that v1, v2, v3, v4, v5 are linearly independent in F8.We need to show that v1, v2, v3,…

Q: Find all values of h such that {t² + 2,5t² + t - 7,-4t² - t + h} is a linearly dependent set in…

A: We are given a set of 3 polynomials in polynomial space P2[t] , including a unknown parameter h And…

Q: The functions y, = e* – e-X a y2 = - 3ex + 2e-x are linearly independent. True False

A:

Q: Consider x1 = et and x2 = v(t)et. If x1 and x2 is linearly independent, then v′(t) = 0. Is this…

A:

Q: Which of the following sets is linearly independent? -ex-y-5=x+C OM= {(1,3),(3,9),(-1,-3)) M=…

A:

Q: Are fi (x) = x, f2(x) = x², and f3(x) = 4x – 8x2 linearly independent or linearly dependent on (-00,…

A: Definition: A set of vectors are said to be linearly independent, if no vector can be represented as…

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

A:

Q: find the linearization at x = a. y = (1 + x2)^−1/2, a = 0

A: We find the derivative of the given function using power rule and chain rule

Q: a. Is S = {v1, V2, V3} linearly independent

A:

Q: Determine if the set of functions {e* , xe* , x²e* }is linearly independent or linearly dependent. O…

A:

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

A:

Q: Show that u = (a, b) and v = (e, d) in K? are linearly dependent if and only if ad – be = 0.

A: Solved below

Q: 2 2) Find a number t such that -3 is not linearly independent in R.

A:

Q: Find the Wronskian of y = 2x + 3, y2 = x² + 3x, and y, = 1 -1. Use the result to determine if the…

A: As per guidelines, we will solve only first question. Kindly repost other question separately.

Q: Suppose vi, v2, ..., m is linearly independent in V and w ɛ V. Show that v1, vz, ..., Um, W is…

A: v1, v2,......., vm is linearly independent in V and w∈V

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: Show that the set {1, x, x2, ..., xn} is linearly independent in Pn(F).

A:

Q: 3. Determine whether the functions e and re are linearly independent or dependent by calculating…

A: f= {e^2x , x.e^2x} is Linearly independent if Wronskian is non zero.

Q: In C[0, 1], are the functions {x2 , x3 , e2x} linearly independent?

A: Linearly dependent and independent functions: Two differential functions f(x) and g(x) are said to…

Q: The functions f₁(x)=e(x+a), f2(x)=e(x+b), and f3(x)=e(x+c), where a, b, and care constants, are…

A:

Q: Let v = and v3 1 for which values of S, v,, V2 , and v3 are linearly %3D V2= %3D indonondont

A:

Q: Suppose that T: R2→ R2 is linear, T(1, 0) = (1, 4), and T(1, 1) = (2, 5). What is T(2,3)? Is T…

A: Given,

Q: Find the linearization L(x, y, z) of the f (x, y, z) = 2/³ + y³ + z³ at the point (1, 2, 3 Answer:…

A:

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: Show that S = 2 is a linearly independent set in R³.

A: Given:     S = 121 , 011 , 201   To show that S is linearly independent set in R3

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.