Express ax? + bx + c as a linear combination of the functions f(x) = 4, g(x) 2x, and h(x) = -x², thus proving that the functions span P,. %3D %3D ax? + bx + c = (-x²) + (2x) + 4

Q: Use the method of substitution to solve the system.

A: To Solve: Use the method of substitution to solve: y=x2-4y=2x-1

Q: x1 – 4x2 dt dx2 4.x1 – 7x2 dt

A:

Q: Solve the system d = dt with a1 (0) = 1 and æ2(0) = -1. %3D

A: The given system of differential equation: x1'x2'=   0-1-1   0 x1x2+t0  ;        x1(0)x2(0)=1-1

Q: Show directly that the given functions are linearly dependent on the real line. That​ is, find a…

A:

Q: If f (x) = x² – 4, what is the simplest form of +1), %3D - X -1 Select one: a. х + 3 о ь. х — 1 c. x…

A: The given function is: f(x)=x2-4

Q: Express ax + bx + c as a linear combination of the functions f(x) = 3, g(x) = 4x, and h(x) = -x²,…

A:

Q: Express ax2 + bx + c as a linear combination of the functions f(x) = 5, g(x) = 4x, and h(x) = -x²,…

A:

Q: Use Cramer's rule to solve the given system of linear equations. 2x1 + x2 - 3x3 = 1x1 - 2x2 + x3 =…

A: 2x1+x2-3x3=1x1-2x2+x3=03x1+4x2-2x3=-5 Here, A=21-31-2134-2,  Ax1=11-30-21-54-2,  Ax2=21-31013-5-2…

Q: Find the real-valued general solution to the following systems of equations x'(t) = %3D

A: Given system is   x't=2-51-2x

Q: If f (x) is a linear function, f (1) = 0, and f (2) = 1, what is f (3)?

A: fx is a linear function such that f1=0 & f2=1

Q: Use Cramer's rule to solve the given system of linear equations. 2x1 + x2 - 3x3 = 5x1 - 2x2 + X3 =…

A: We have to use Cramer's rule to solve the given system of linear equations.…

Q: Show that if f and g are linear, then so is f + g. Is the same true of fg?

A:

Q: find a formula for the linear function f(x) that satisfies f(5)=7 and f(0)=-3

A: Given information:f(5)=7 and f(0)=-3

Q: find the interverse of the fuction f (x)= 2x + 3/x-4

A:

Q: Use Gauss-Jordan reduction to solve the system of equation below: X1 + X2 + 2x3 = -1 X1 – 2x2 + x3 =…

A: Solve the equation

Q: Use Cramer's rule to solve for X2 in the given system. 5x,-2x,+X3=1 X2+X3=0 X1+6x,-X3=4

A:

Q: Show directly that the given functions are linearly dependent on the real line. That is, find a…

A: Given function is  f(x)=6xg(x)=5x2h(x)=9x-12x2 Definition: If n functions f1,f2,f3,...fn are said to…

Q: Use Cramer's rule to solve the given system of linear equations. x1- x2 + 4x3 = - 2-8x1 + 3x2 + x3 =…

A: Solution: Consider the given system is x1-x2+4x3 = -2-8x1+3x2+x3 = 02x1-x2+x3 = 6 We have Cramer's…

Q: Which is equal to () (x) given that g(x) = 1 – 3x and h(x) = Vx? %3D Vx – 3xVx 3xVx Option 1 Option…

A: Let's find.

Q: True or False? If the functions Yı and y2 are linearly independent solutions of y/" + p(x)y' + q(x)y…

A:

Q: Show directly that the given functions are linearly dependent on the real line. That is, find a…

A: Use the given information.

Q: Solve the linearsystem by GE method x- 2y + 3z 9 -x + 3y = -4 2x - 5y + 5z 17

A: First of all we will find the augmented Matrix and then through use row operations to solve the…

Q: The function of two variables f(x.y)=(y-2) x^2-y^2 has:

A:

Q: Show that if f and g are linear, then so is f + g. Is the same true of f g?

A: Let f,g:V→V are linear maps To show that f+g and fog are also linear

Q: Find the linearization at x = a. g(x) = 20x² x - 3 a = 12

A:

Q: Given that x3y2=ax+y, express y′ in terms of x and y (a is a constant

A: Given x^3y^2=ax+y'

Q: 1. 3X1 + 4X2 = -2 5X1 + 3X2 = 4

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 4. Examine if functions f(x)= x , f2 (x) = x², f;(x)=x² – 2x are linearly independent.

A:

Q: If f(x)=/2x and g(x)=1-x², then (gof)'(x)= %3D

A: =>(g.f)(x)=g(f(x))

Q: Use Cramer’s Rule to solve (if possible) the system of linear equations.

A:

Q: Find the linearzation L(x) of f(x)= \sqrt(5x+16) at a=0

A: Given Fx=5x+16 at a=0The objective is to find the linearzatin Lx ofFx=5x+16 at a=0find the…

Q: Which is equal to (4) (x) given that g(x) =1 – 3x and h(x) = Vx? %3D Vx – 3xVx - 3xVx X. Option 1…

A:

Q: f(x) = 2x, g(x) = 3x², h(x) = 5x – 8x²

A:

Q: Find the solution for for nonlinear equation system below: F1 (x, X:) = x, + x;'e$l – 2 F2 (x1, X2)…

A:

Q: Solve the following system by conjugate gradient method. [4 2 2 1 -1 [1 1] [X1] -1 1||X2 1||X3 3]…

A: Given system: 421123-111-1211103x1x2x3x4=1201 Let A=421123-111-1211103 and B=1201 Assign X0=0000

Q: The x-intercept of the linear function f(x) = 4x + 16 is %3D -0.55 O-20.52 O 13.24 O -4.00 O 1.80

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find the solution for for nonlinear equation system below: F1 (x,, X2) = x, + x,'e$l – 2 F2 (x, X;)…

A: Given non-linear equation system isF1x1, x2=x12+x22e-5x1-2F2x1, x2=x22+x12e-7x2-1x10=3,    x20=2

Q: Solve the following systems of linear equations using the RREF function on the calculator. show…

A: We need to solve the following systems of linear equations using the RREF function on the…

Q: Find a general solution of the system?

A:

Q: Use Cramer's rule to solve the given system of linear equation. a11 x1 + a12x2 = b1a21X1 + a22x2 =…

A: Consider the following system of equations, a1x+b1y=c1a2x+b2y=c2 Then using Cramer's rule, x=DxD and…

Q: Solve the following system of linear equations using Crammer's rule: X1-2x2+3x3=-2 -х1+x2-2х3-3…

A: A system of linear equations are given. We need to solve it using Cramer's rule.

Q: The maximum number of linearly independent solutions of y" -2y"'+xy = 0 is 3. Select one: True False

A: y''''-2y'''+xy

Q: Show that the three functions: f₁(x) = ex-8f₂(x) = exf3(x) = 4(2x-2) are linearly dependent.

A:

Q: Find gof. f(x) =x², g(x)=x- 4 († +zx) O

A: Find gof

Q: Find the set of solutions for the given linear: -9x1 + X2 + 9X3 = 1 5x3 + X4 = -3 - (X1, X2, X3, X4)…

A: Consider the following system -9x1+x2+9x3=1          .....(1)       -5x3+x4=-3       .....(2)

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

A: Given:

Q: Are functions f(x) = x² – 2, g(x) = x² + 2x – 1 and h(x) = 2x² + 6x + 1 linearly dependent? If yes,…

A: Let f(x), g(x) and h(x) are linearly dependent.  So, we can write: Then we compare both sides

Q: Express ax? + bx + c as a linear combination of the functions f(x) = 5, g(x) = 4x, and h(x) = -x²,…

A:

Q: If ρ = 0, then the two variables under consideration are linearly ________.

A: