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Components and equality Define the points P(−3, −1), Q(−1, 2), R(1, 2), S(3, 5), T(4, 2), and U(6, 4).
26. Find the equal
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Calculus: Early Transcendentals, 2nd Edition
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- 2. For a n-vector x, and X1 + x2 X2 + x3 y = Ax = Xn-1 + Xn a) Find A b) Are the columns of A linearly independent? Justify your answer? c) Are the rows of A linearly independent? Justify your answer?arrow_forwardGenerate 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.arrow_forwardProblem 5. Let u = g – g(-), where g-) = (g-1, 90, 91,...,gr-1). Interpret the physical meaning of the vector u.arrow_forward
- 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.arrow_forward. Consider the following vectors: A = a +2âμ-âμ ul B=5a-3a3 ul C=7a-4a2-2â³ Ful u2 D=-â+2a3 ul a) For vectors B,C,D, obtain both sides of the BAC-CAB rule and show the validity of the relationship. b) obtain the result of (A×B)×(Č×D). c) obtain the result of (AxB).(Č×D) d) obtain the results of B⚫(Č×D), Č·(Ď×B), D.(B×Č) e) obtain the magnitude of the vector A+B+C+D.arrow_forwardUse 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 varrow_forward
- 4. Consider the set V of vectors (x, X2, X3, X4) ER such that X1 + x3 = 0 and x, + x4 = 0. a) Prove that V is a subspace of R*. b) Give a basis and the dimension of V.arrow_forwardPerform the following Matrix Operations for the predefined matrices. Given the System of equations: 2х + 4y — 5z + Зw %3D —33 3х + 5у—2z + бw %3D — 37 х — 2у + 4z — 2w 3 25 Зх + 5у-3z + Зw = -28 Write the systems as Ax = b, where A is the coefficient matrix and b is the vector for the constants. 1. Encode the Matrix A and the column vector b. 2. Solve for Determinant of A. 3. Find the Inverse of A. 4. Form the Reduced Row Echelon of A. 5. Find the number of rows and number of columns of Ab. 6. Find the sum of the columns of A. 7. In each of the columns of A, find the highest values and its indices. 8. Augment A with b; 9. Find b\A 10. Form the Reduced Row Echelon of Ab. 11. Extract the Last Column of the Reduced Row Echelon Form of Ab. 12. Create a matrix A whose elements are the same as matrix A, but the first column is the column vector b. 13. Create a matrix A whose elements are the same as matrix A, but the second column is the column vector b. 14. Create a matrix A whose elements…arrow_forwardIs W a subspace of the vector space? If not, state why. (Select all that apply.) w is the set of all vectors in R° whose components are Pythagorean triples. (Assume all components of a Pythagorean triple are positive integers.) O w is a subspace of R°. O w is not a subspace of R because it is not closed under addition. O w is not a subspace of R³ because it is not closed under scalar multiplication.arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
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