Two vectors from the vector space described in the previous prob- lem (polynomials defined on the interval [-1, 1]) are 1+1 and 1-1. Find an orthogonal set of vectors based on these two vectors.
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- Let v be a vector whose coordinates are given as v = [vx, Vy, Vz. If the quaternion Q represents a rotation, show that the new, rotated coordinates of v are given by Q(0, Vx, Vy, Vz)Q*, where (0, vx, Vy, Vz) is a quaternion with zero as its real component.Prove that in a given vector space V, the zero vector is unique. Suppose, by way of contradiction, that there are two distinct additive identities 0 and u,. Which of the following statements are then true about the vectors 0 and u,? (Select all that apply.) O The vector 0 + u, is not equal to u, + 0. O The vector 0 + u, is equal to un: O The vector 0 + u, is not equal to 0. O The vector 0 + u, does not exist in the vector space V. O The vector 0 + u, is equal to 0. O The vector o + u, is not equal to u: Which of the following is a result of the true statements that were chosen and what contradiction then occurs? O The statement u, + o 0, which contradicts that u, is an additive identity. O The statement u, +0 # 0 + u, which contradicts the commutative property. O The statement u, = 0, which contradicts that there are two distinct additive identities. O The statement u, + 0 U, which contradicts that O is an additive identity. O The statement u, + 0 + 0, which contradicts that u, must…Thank you but I need it without using vectors
- Simplify the following functions using a k-map.Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 - V1, 4V1 + 5v2), v = (1, -2, -3), w = (3, 9) (a) the image of v (b) the preimage of w (If the vector has an infinite number of solutions, give your answer in terms of the parameter t.)6. Using the root vectors, work out the weight diagram of 10.
- Problem 5. Let u = g – g(-), where g-) = (g-1, 90, 91,...,gr-1). Interpret the physical meaning of the vector u.Let V₁ a) show that none of vectors V₁, V₂, and V3 can be written as a linear AME combination of the other two, i.e., show that the only linear combination which gives the zero vector ₁V₁ C₂V₂ + C3V3 = 0 is where, C₁ C2 C3 = 0. b)) show that each of vectors V₁, V2, V3, and V can be written as a linear combination of the other three, i.e., find the constants c₁, c2 and c3 in the linear combination G₂ V₁ + G₂V₂ + 3V3 = V₁ such that not all c, are zeros. V4Use a simple algorithm to do the following ant it as a matlab code 1. Determine the mean of the elements of a matrix A WITHOUT using the mean function 2. Find out how many non-zero elements a matrix A has 3. Sum the diagonal elements of a square matrix A 4. Add the first and last elements of a vector v if you are not given the length of v
- MATLAB question For input vector x, write a function to check whether there exists exactly 4 elements in x which are divisible by 3.Generate H (Hilbert Matrix) for n = 15.Compute the right-hand size vector b = Hx so that the exact solution is xˆ = 1 (thevector of ones). Solve the linear system in MATLAB as a least squares problem usingSVD and report the relative error in the approximate solution in the Euclidean norm.Compare your result to the solution obtained by H\b.USING PYTHON A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal (i.e., ai,j where j = i) and the ones immediately above and belowit(i.e.,ai,j wherej=i+1orj=i−1). Write a function that solves a linear system whose coefficient matrix is tridiag- onal. In this case, Gauss elimination can be made much more efficient because most elements are already zero and don’t need to be modified or added. Please show steps and explain.