Create an orthonormal set of polynomials using the set { 1, x, x^2 } by the Gram -Schmidt process.

Q: Use the given real ZERO of the polynomial function to find the remaining real ZEROS. f (x)= 380x² +…

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Q: Find a linear funtion P(z) = a + a₁ which gives the best least squares fit for the following points:…

A: Given the points -4,0, -2, -2, 4,-9, 5, -8. Now,  x y x2 xy -4 0 16 0 -2 -2 4 4 4 -9 16 -36…

Q: Find QR decomposition

A: Consider the provided matrix A,

Q: Evaluate W(1 + x, x, x^2

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Q: Linear Algebra: Consider the polynomials p1(t)=1+t^2, p2(t)=t, p3(t)=t−t^2. Is {p1,p2,p3} a…

A: Consider the polynomials p1(t)=1+t^2, p2(t)=t, p3(t)=t−t^2.

Q: For all a, b in R, show that -max{a^2, b^2} <ab max{a^2, b^2}.

A: To prove that for all (a,b)in(R), [max(−a2b2,ab)≤ab≤max(a2b2)] We'll consider three cases: 1.…

Q: What element corresponds to (2,3) of (A^T) x (B^T)? What element corresponds to (3,1) of (AxB)^T?…

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Q: Find a polynomial P(z) = a + a₂z+ª₂x² of degree 2 which gives the best least squares fit for the…

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Q: Determine the linear Lagrange interpolating polynomial that passes through the points (2, 4) and (5,…

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Q: Determine the third degree Newton polynomial which passes through the data points (0,1); (1, 0); (2,…

A: The objective is to determine the third degree Newton polynomial which passes through the data…

Q: Find the third degree Taylor Polynomial centered at x = 0 for f(x) = x^2√1 + 4x.

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Q: find

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Q: Construct a polynomial from the data (1,4),(3,14)(5,19),(7,21),(4,23),(11,21) and also find…

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Q: Find the integer a in Z5 so that (x-a) become a divider for f(x)=x^3+2x^2+3x+3 over Z5[x]

A: We have to find an a∈Z5 such that x-a is a divider for the polynomial fx=x3+2x2+3x+3 over Z5x. If…

Q: Why the minimal polynomial x^2 - (sqrt(2)+sqrt(-2)) splits into linear factors over K?

A: Assume K is a field that includes the square roots of both 2 and -2. The formula for the element  α=…

Q: Calculate the 1st order Newton polynomial that interpolates the two data points (1,1),(2,3). Now…

A: We can use Newton's forward difference interpolation method to find Newton's polynomial.

Q: (i) X= “ABCDBCDC” and Y=” BCDCD” (ii) X= “POLYNOMIAL” and Y= “ EXPONENTIAL”

A: This is a problem of counting and finite math.

Q: Orthogonalize {1, t, t²} in P₂ (R) with 1 (f, 9) = ["ª, f(x)g(x) dx. -1 Then normalize each one so…

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Q: why the minimal polynomial x^2 - (1+sqrt(2)) does not split into linear factors over K?

A: Let K be a field  . Then a polynomial f(x)∈K[x] splits into linear factors in K if K contains all…

Q: Verify if the following polynomials are irreducible over Q. p1(x)=x^3-4x^2+3 p2(x)=x^3+4x^2+3…

A: From Einstein criteria we sole this

Q: Factor the polynomial x^4 + x^3 + x^2 + x completely into irreducible polynomial in Z_2[x]

A: Factor the polynomial  completely into irreducible polynomial in .

Q: Determine the value of k such that (x^3-2kx+1)/(x-k ) has a remainder of 0.

A: f(x)=(x^3-2kx+1)

Q: Find a 5th degree polynomial with zeros x = 3 + 2i, 1 − squareroot2, and −1 with a co-efficient of 4…

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Q: Determine the number a in Z5 so that (x - a) becomes a divisor of f (x) = x ^ 3 + 2x ^ 2 + 3x + 3 in…

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