Orthogonal vectors - Study guides, Class notes & Summaries

CHE505 – Math Exam with Questions and Answers 1. What is a well-conditioned system? How do you determine this mathematically? ANSWER Small perturbations in input don't result in large changes in output, so the solution is not sensitive to system parameters. cond(A) = ‖A‖‖A⁻¹‖ ≤ 1 ‖δx‖/‖x‖ ≤ cond(A) ‖δb‖/‖b‖ 2. What is the projection of vector y onto vector x? When is performing this useful? ANSWER proj_x(y)=(<x,y>/<x,x>)x Orthogonaliza...

Contents Preface iii 1 Linear Equations and Matrices 1 1.1 Systems of Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Matrix Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Algebraic Properties of Matrix Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.5 S...

MAT1503 Assignment 5 2023 100% TRUSTED workings, explanations and solutions. For assistance call or whatsapp us on +25477 954 0132 . Question 1: 12 Marks (1.1) Let U and V be the planes given by: (2) U : λx + 5y − 2λz − 3 = 0, V : −λ x + y + 2z + 1 = 0. Determine for which value(s) of λ the planes U and V are: (a) orthogonal, (2) (b) Parallel. (2) (1.2) Find an equation for the plane that passes through the origin (0, 0, 0)and is parallel to the (3) plane − x + 3y − 2z = 6...

Jacobian How to use the chain rule? When you have a composition of functions (dw/ds, dw/dt)= (df/du, df/dv)(du/ds, dv/ds, du/dt, dv/dt) so it gives a vector Classify critical points 1. differentiate WRT each variable x and y. 2. set them equal to 0. then solve for the values (often take the equation that is easy to factorize and take its values. 3. replace the values obtained in the other partial equation set equal to 0 to get the points ***trick: you can add the equations some...

GISP Study Already Graded A+ Georeferencing and Control Points - Georeferencing: The process of associating a map or image with spatial coordinates to accurately represent its geographic location. - Control Points: Specific points that correspond in pairs, matching known spatial locations to points on an unreferenced image or map. Spatial Reference Systems - Spatial Reference System (SRS): A coordinate-based system—local, regional, or global—used to locate geographical entities, al...

MAE101 TEST 3 WITH ALL QUESTIONS AND ANSWERS ...

Component Form Correct Answer The form of a vector that lists the vertical and horizontal change from the initial point to the terminal point <__,__> Magnitude of a Vector Correct Answer The length or size of a vector. It is a scalar value calculated by the square root of (u1^2 + u2^2 + u3^2) Unit Vector Correct Answer A vector with length 1. u / |u| Equal Vectors Correct Answer Vectors with the same component form Parallel Vectors Correct Answer Vectors with the same or oppos...

Fourier Series Exam Questions With Correct Answers. A function is periodic if.. - answerf(x+P) = f(x) What is the least period of a function? - answerThe smallest value for P for which f(x+P) = f(x) What is a Fourier series? - answerA way of writing almost any periodic function as a sum of trigonometric functions/sinusoidal oscillations with frequencies integer multiples of the fundamental 1/P (harmonics) Done by identifying a complete set (basis of functions) to identify all elements in...

Linear Transformation correct answer: A function T from Rm to Rn is a L.T if there exists an n x m matrix such that T(x)=Ax for all X in vector space Rm The columns of the matrix of a linear transformation correct answer: The matrix of transformation has column vectors T(e1), T(e2), etc. where e's are the standard vectors Linear Transformation(proofs) correct answer: 1) T(kx)=KT(x) 2) T(x +y)=T(x) +T(y) (x and y in Rm (starting Vector space) and K is a scalar ) Distribution Vector...