9(2): het f) = x'+3x²- ax+ a and g(4)=x+2x+ 1 E Q [x]. Find the Unique.poly nomials Such that flx) = q,(x)_g(x)+ Y(x) where qcx) g x(x)E Q[x] either y(x) =0 or os deg x6x) Ss deg glx).

Q: IT X) IS defined as foilows, ina (a) i( – 2), (D) (U), and (C) I(2). x? if x 0 (Simplify your…

A: Since the given function is a piecewise function therefore we need to take care of the branch of the…

Q: Assume xo = x2 – 2h, *1 = 12 – h, a3 = x2 + h, 24 = x2 + 2h Use the undetermined coefficients method…

A: To solving the system we use the Gaussian Eliminating and back substitute method

Q: (15) If X-exp(1), then (a) 2X-exp(2) (c) 2x~exp (¹) O a O b O C Od (b) 2X-X² (2) (d) 2X-G(2,1) is

A: Given that X~exp(1) then  We have to find 2X follows which distribution:

Q: 3. FIND THE ROOT OF fcx)= x*+ 3x? - 3メ -3 x°+ 3x?- 3×メ -3 USING SECANT METHOD メi=1 TEN DECIMAL…

A: consider the function f(x)=x3+3x2-3x-31st iteration :x0=1 and x1=2f(x0)=f(1)=-2 and…

Q: Q12: If x + y = 10, then the largest possible Q13:The absolute maximum value of A) has no absolute…

A: Since, we have been asked to solve question-(13) in which our aimis to find the absolute maximum…

Q: A natural cubic spline is defined by Sa,(x-1)' +b,(x-1)² +c, (x - 1) + d, S(x) =- if 0sxs1 (x- 1)' +…

A: Step:-1 Since, we know for cubic spline S(x)=S0x=a0x3+b0x2+c0x3+d0…

Q: a(bx+j)(cx+k)(dx+m)² (ex+n)(gx-p)(hx+q)' with the following conditions a,b,c,d,e,g h.j,k,m,n,p.q are…

A: Given type of function is fx =abx+jcx+kdx+m2ex+ngx-phx+q

Q: Check that x(x + 1) − y(y + 1) = (x−y)(x+y+1) then find all possible r such that x(x + 1) = y(y + 1)

A: We need to validate the equation: x(x+1)-y(y+1)=x-yx+y+1. We also need to determine the values of x…

Q: Given that P(X)= P(Y)= and P(XUY)= find 20 20 10 a) P(XnY) b) P(XIY)

A: Given,PX=920PY=720and PX∪Y=710

Q: O f(x) = x3-6x²+9x+1 funct lon is given d) Find the equation f@ =0 `s real rost with linear…

A:

Q: a) Get the (2n+1)x Pn (x) = (n +1) Prar tx) +o Pau (x) reconnection polynomials using the; P(x, 2)=…

A:

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: rove if the ff. arguments are valid using any formal proof of validity. vx, (P(x) v Q(x)) vx,…

A:

Q: Evaluate the Cauchy principal value of 2 x 50% -dx 8 x 2 (x² + 1)²

A: We have to find Cauchy Principal Value of the given integral.

Q: Q.2 If f(x) = 2*, Then show that a) f(x+3) – f(x – 1) =f(x) S(x+3) S(x-1) = f(4) b) %3D

A:

Q: f₁ = x4 f₂ = -x4 f3 = x² f4 = -x²

A:

Q: 4 – x lim X → 4 5- Vx² +9

A: We have to find the limit

Q: Find a bijection between the following sets: (a) (8,00) and R. (b) (-8, 8) and R. (c) {-1,1} x N and…

A:

Q: Th nction f(2) = (2z3 + 8z) (z – 2i)(z + 5i)2 has a pole at z = -5i. :Select one True False

A:

Q: (a) Determine whether f(z) = 91³ -21³ +18z-50 is irreducible over R.

A:

Q: 3. h(x) = -2x³ + 5x² + 4x° – 3x + 12x? - 4 !! f (x) f(x) →_ as x → -00 as x → +00

A: We have to find the limit of the given function.

Q: 3. (a) Find a unit in Z[√2] which is not equal to 1 or -1. Hint: Use 1 (b). (b) (*) Show that Z[√2]…

A: The objective of the question is two-fold. First, we need to find a unit in the ring Z[sqrt(2)] that…

Q: I(¥x (P(x) v Q(x))) ^ (Vx (¬Q(x) v S(x))) ^ (Vx (R(x) → ¬S(x))) ^ (3x ¬P(x))] → 3x ¬R(x)

A: Given: To do: Prove the above statement.

Q: Let S,(x) = 2x³ – 3x² + 3x – 4, 0<x < 1, S,(x) = x³ + b,x² + c,x + d,1 sxs 2. Find b,, C1, d, that…

A:

Q: Q2) If f (x) = x + 5 and g(x) = x² – 3, find the following: %3D 1) f(f(x)) 2) g(f(x)) 3) f(g(x)) 4)…

A: Given that: f(x)=x+5          and    g(x)=x2-3

Q: 1 s) Let f(x, y) = x¹y-²-5ry- ? (graye ! 'e' e7 In (2ry), find fzz, fyy, fry, and fyz. Sadda

A:

Q: The quadrature rule [“ f(x)dx = w₁ f(x1) + w2f(x2) + E (2) -h can be made exact for all cubic…

A: Given Information:The quadrature rule is given as .Objective:Write the four equations satisfied by…

Q: Calculate GCD(x3 + 2x2 + 3x , x2 + 3x + 2) in Z5 [x]. What is wrong with my answer? The correct…

A:

Q: Let X be N(0, 1)and Y be N(0, 9) , with X and Y independent. Let Z 2X – 16Y, and let W = 3X3 + 4Y5…

A:

Q: The maximum error for F=yx2+y+y2 are |(2xy)Ax| +|(2y+1 + x²)Ayl |(2x + y)Ax| + |(2y + x)Ayl x|Ax|…

A: Given function is, F=yx2+y+y2

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.