If the Wronskian of the DE: Py" + xp(x)y + 3y = 0 is et Then p(x) = %3D O -2x O -2r O 3r* O 3xe O-3xe O -3r O-3r O2r O-3

Q: Show directly that f(n) = n2 + 3n3 Î (n3). That is, use the definitions of O and W  to show that…

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Q: Let f(r) = ([r] – 1)² and g(x) = . Then the domain of go f is %3D %3D Select one: O (-00,0) OR\{1} O…

A: To find the domain of gof forf(x)=x-12g(x)=1x

Q: Find the first piece S1 (x) of a natural cubic spline that interpolates the set of points (0,1),…

A: Formula for cubic spline interpolation is…

Q: 3. Determine a and b for Y X1 and Y2aX bX2 such that EX1 EX2}= 0, Var(X) Var(X2) Var(Yi) Var(2) 1,…

A: The provided information is:

Q: ○A. T(A) = 3A from R6×4 to R6×4 -9 9 B.T(A) = A [72] [173] 4 5 ASA-¹ from R2×2 to R²×2, where S A…

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Q: The f e²x +e-2x e2x-e-2x dx is -2x1 {A}={In 2x te e e2x-e-2x + C 2x {B} In|e²x −e-²x | + C {C} -2…

A: To solve the given integral using substitution.

Q: Let p be a prime and let q = p". Let f(x) = x³+ax+b € Fq[x] be

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Q: 7. Evaluate * (D5 - 3D4 + 8D³ + 16D² - 9D - 13)y = 0 y = (C₁ + C₂x)e¯x + С3ex +C4e²x cos3x + C5e²x…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Given u(x)= x +3 and v(x)= 9x – 4, find u v. O 9x² – 12 - O 9x² + 27x – 4 O 9x+ 23 x - 12 O 9x + 23…

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Q: Let P3 have the inner product given by evaluation at -3, -1, 0,1, and 3. Let p(t) = t? and q(t) = 2t…

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Q: (х, 2x2, —х3)

A: We have to solve given problem:

Q: Which of the following vectors are orthogonal under the standard inner product? 2 -=[] [1] u= and v=…

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Q: Let [2 . -3 1 X = |2 -1 4 det(X) - then %3D

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Q: e multiplicative inverse of 1+ 3x in Z,[x] is: 4x+1 None 1/(3x+1) 6x+1

A: Consider the given information: To find multiplicative inverse of  1+3x in ℤ9x.

Q: The domain of f(x) = /x + 1 - – /1 – x is O [-1, ∞) O (-∞, 1] O (-∞, –1] U [1, ∞) O [-1, 1] None of…

A: We need to tell the domain of the given function: f(x)=x+1-1-xFor calculating the domain, the…

Q: 3. Evaluate the integral / Vr+3 (x- 1 4 4 (a) 극(z +3)72-(r + 3)52 + 국(2 +3)%2 +C 1 4 (b) (r + 3)"…

A: This question is related to Indefinite integration, we will solve it using given information.

Q: (15.2): Find In(x) – In(x² – 1) +2 In(z +3) 3

A: Find 13ln(x)-lnx2-1+2lnx+3. Logarithmic properties used: alogcb=logcba logca-logcb=logcab…

Q: Differentiate: f(x) = 4x³ - (5/x²) %3D O a. f(x) = 12x2 - (10/x³) O b. f(x) = 12x2+ (10/x³) O c.…

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Q: Q.4) The Wronskian W(e-x, e*, e2x), is: a) 6e% Q.5) The general solution of the equation yto + 9y" =…

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Q: If gcd( m,91) = gcd(n, 91) = 1 %3D %3D

A: Given, if gcd(m, 91)=gcd(n, 91)=1,  To prove that                     91|m37-n37

Q: b₁ + x b₂ + x b3 + x + +x\ C₂+x, then show that A'(x) = 0 a₁ + x If A(x) = a₂ + x a3 + x C3 + x and…

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Q: 1-4x-51+36 x7 x11/4 x-11/4 O O O O

A: We have to solve the given inequality.

Q: Evaluate : | [6x-1+ 2 e2 + 4" – 9] dæ In(x)° + e2" + In(4) 9x + C, Where C is the parameter 4* O…

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Q: Let n P₁ P2 = ppp be the prime factorisation of an integer n > 1. 1: ti A 11. C.

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Q: Question 3 Is f(x) = x4n-2 - x4n-4 + x4n-6 + ...+ x² - 1 divisible by g(x) = x4 – 1? %3D

A: Binary operations like addition, multiplication can also be performed between two polynomials. When…

Q: Find all second-order three-step methods in the form Yn+1 = aoyn+q₂yn-l + a₂yn-2 +h[b_f (tn+1• Yn+1)…

A: Second-order three-step methods in the form you provided are used to solve initial value problems…

Q: Spring 2021 # 4. Let p(z) = 2+ 32 + 6. (a) Show that p(z) has three zeros (counting multiplicity) in…

A: Given :  It is given that,  p(z) = z4+3z3+6. To show :  We have to show the following statements ;…

Q: Which of the following is indeterminate at x = 1? x² + 1 x2 – 1 x2 – 1 Vx +3 - 2 x2 +1 Vx + 3 – 2 x…

A: We plug x=1 in each expression

Q: Let T: P3 R³ be defined by T (αo + a₁x + a₂x² + a³x³) {0.00} 3 G and C = Given [7] Pc (T(u)). Pc…

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Q: 4-8y² (a) ſ dzdydx 0 0

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Q: Let T: P3 → R³ be defined by T (ao + a₁x + a₂x² + а3x³) {6.0·8} and C= 2 = 0 Given [7] Pc (T(u)). 4…

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Q: Determine if x¹ + x² + x + 1 is irreducible in Z[x].

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Q: Let f(x, y) = In(x²y), where a = s² + t² and y = 2s + 3t. %3D Which of the following is a correct…

A: Given,           f(x,y) = lnx2y3,  where x = s2 + t2 and y = 2s + 3t

Q: the system of inequalities. O x+ ys30 x2 10 y2 10 O 2x + ys 30 x2 10 yz 10 O x+y2 30 X< 10 y< 10 O…

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Q: Expand In t(x²+1) (x+2) (x-s)² X-5

A:

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.