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Linear Algebra: Matrix of Transformation.Are the following examples linear transformations from p3 to p4?
Complete the proof of the question “For which odd primes p is LS(2, p) = 1?” by showing that (2/p) = -1 if p = 5(mod 8) and that (2/p) if p = 7(mod 8).
Linear Algebra: Vector Spaces.Consider R2 with the following rules of multiplications and additions: For each x=(x1,x2), y=(y1,y2):
Why is the set of Natural numbers an infinite set, but the set of blades of grass outside your residence a finite set? Explain.
Explain what does palindromic polynomials means? Give me examples palindromic polynomials with even and odd degree.
Linear Algebra and Numerical Analysis.Questions on a Sequence of Polynomials.
Find the polynomials that represent 1/x^3+x , x/x^3+x, x^2/x^3+x, and x^3/x^3+x modulo the irrreducible polynomial x^5+x^2+1 over F2.
Prove that there are no integers x, y, and z such that x^2 +y^2 + z^2 = 999
''Annuities are not a wise choice for certain investors''. Do you agree with that statement? Write a brief paragraph explaining why or why not.
Show that if the roots of the polynomial p are all real, then the roots of p' are all real. If, in addition, the roots of p are all simple, then the roots.
If W is a set of one or more vectors from a vector space V, then W is a subspace of V if and only if the following conditions hold.
Consider the vectors 1 and x. Find the angle theta between 1 and x. Determine the vector projection p of 1 onto x
Linear Algebra: Vectors - Inner Product.Show that the functions x and x^2 are orthogonal in P5 with inner product defined
Show all work including how eigenvalues and eigenvectors are derived.
The Lucas numbers Ln are defined by the equations L1 = 1 and Ln = Fn+1 + Fn-1 for each n > or = 2
Algebra equations.Determine whether each of the following is a function or not.
If R is a unique factorization domain and if a and b in R are relatively prime (i.e.,(a,b) = 1), whenever a divides bc, then a divides c.
How would you find a basis of the kernel, a basis of the image and determine the dimension of each for this matrix? The matrix given below.
Perform the indicated operation. Find the opposite of the polynomial.
Mr. Smith invited 17 guests to his "Disco-reunion" party. He assigned each guest a number from 2 to 18, keeping 1 for himself.
It is important to simplify radical expressions before adding or subtracting to get terms with like radicals. Once we find terms with like radicals.
How to find rank of a matrix: definitions and an example (4*4 matrix) with detailed explanations.
Prove that if every even natural number greater than 2 is the sum of two primes, then every odd natural number greater than 5 is the sum of three primes.
Proof : Diagonalization of Matrices.Write a proof for the following statement:
The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and + 4i among its roots.