- Show that the polynomials {1, x, x²,x³} are linearly independent set in P3.

Q: Determine whether each set {p1,p2} is a linearly independent set in P^3.  1) the polynomials…

A: The given points are, p1t=2t+t2p2t=1+t Consider the table as shown below.   p1t=2t+t2 p2t=1+t…

Q: 1. Find an orthogonal change of variables that eliminates the cross product terms in the quadratic…

A: Given Q=x12-4x1x2+x22

Q: Let B={(1,-2,1), (4,-7,5), (5,-8,8)], and x=(-6,10,-7) Find [x]B

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Q: Determine integers x and y such that (а) gcd(51, 288) — 51х + 288у (b) gcd(357, 629) = 357x + 629y

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Q: Which of the following are continuous and piecewise polynomials with respect to the nodes o, x1, x2,…

A: Continuous and pocewise continuous of the polynomial

Q: 7 Determine whether the set {1, x, x²} is linearly dependent or in- dependent in R (Justify your…

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Q: Use the inner product = aobo+ aıb1+ azbz+ asb; to find , lIlp|], d(p, q), and then find the angle…

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Q: positive real numbers such tha ith proof the minimum value of

A: Given, x,y,z be a positive real number such that x4+y4+z4=1.The minimum value of…

Q: Let a0, a1, a2, a3, a4 be constant real numbers such thata0/5 + a1/4 + a2/3 + a3/2 + a4 = 0.Show…

A: Consider−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−f(x)=5a0​x5​+4a1​x4​+3a2​x3​+2a3​x2​+a4​x.with  input from…

Q: Express (a) v = 3t² + 5t – 5 as a linear combination of the polynomials: P, =t² + 2t +1, P, = 21² +…

A: Suppose is a vector space . Dimension of  vector space is 3. The standard basis of vector space is…

Q: Does the following set of polynomials {t? + 1, t2 + t,t + 1} span P2?

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Q: Ex.5 - Prove that the polynomial 2ª + z + 1 has exactly two zeros in the right half-plane.

A: Solution: We will be using the method of Routh array For a polynomial Qz=anzn+an-1zn-1+...+a1s+a0…

Q: Find the unique quadratic polynomial y = ax² +bx+c that passes through the three points (1, 1),…

A: What is Polynomial: A polynomial is a real valued function. It is an algebraic function that is…

Q: Use Newton’s Divided Difference Formula to interpolate f (1), if the polynomial has given points…

A: We have to interpolate f(1) using Newton's Divided Difference Formula.

Q: {₁,...,} is linearly independent if and only if {₁,...,} is an orthogonal set. True False

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Q: Use coordinate vectors to test whether the following sets of polynomials span P, Justify your…

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Q: Are the polynomials x? + 1,x? – 1, 2x – 1 linearly independent in P2?

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Q: Count the number X of functions y: (20, 21,..., 23) → (5,6,...,8) so that is not onto. X =

A: Given function φ:(20,21,...,23)→(5,6,...,8)

Q: Prov that Let A be a fuzzy ideal of R, anand by Lemma- be fuzzy singletons. Then (a.b) no A = anobu…

A: To prove that (a⋅b)h ⋅A=ah ⋅bh ⋅A given A is a fuzzy ideal of R and ah , bh are fuzzy singletons, we…

Q: Compute the complement of relation R. R={(1, 1), (5, 1), (5, 5), (6, 1), (6, 6), (7, 1), (7, 7)}

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Q: Write x3 + 2x + 1 as a product of linear polynomials over someextension field of Z3.

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Q: Let P0. (x) denote the quadratic polynomial that interpolates the data {(xo, yo), (x1, y1), (x2,…

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Q: consider the relation R={(1,a),(1,b), (3,b),(3,d), (4,b)} form X={1,2,3,4} and Y={a,b,c,d}. Thus…

A: Consider the relation

Q: Consider the polynomials P, (1) = 1 + 1² and p2(1) = 1 – 1². Is {p · P2} a linearly independent set…

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Q: 2. Let V be the set of all ordered pairs of real numbers, and consider the following addition and…

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Q: az Q.7 If z(x + y) = x2 + y?, show that lax = 4 ду. - +(1 - ax ду.

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Q: - - Do the polynomials t³ + t +2, t² − t +2, t³ +2, and −t³ + t² − 5t +3 - span P3? (Give support…

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Q: Use the inner product (o, 9) = 2obo +a1b1 +a2b2 to find o, 9), |P||- |||, and d(p, a) for the…

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Q: 2. Determine whether the set S = {(2, 0, 1), (2, -1, 1), (4, 2, 0), (-6, 2, 3)} a. Spans R3 b. Is…

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Q: Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} %D are two sets. find R = {(x, y): x EX and * y EY and…

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Q: z+1

A: Given: z+1z2+12 Let, fz=z+1z2+12 Or, fz=z+12z2+12 The zeroes of f(z) are given by:…

Q: Represent the following relation {1,2, 3, 4} with a matrix. {(1,1), (1, 4), (2, 2), (3, 3), (4, 1)}

A: Given below the detailed solution

Q: (b) Are the polynomials x + 5, x – 5, 2x +1 linearly independent in P1(R)? Explain.

A: The vectors a1, ..., an are called linearly independent if there are no non-trivial combination of…

Q: Find the standard inner product on P of the given polynomials. p= -2+ 4x + a2, q = 3+ 4x 3a2. (p, q)

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