Solve the system Ux = y for x. U = ? X = ? If the nxn matrix A can be expressed as A = LU, where L is a lower triangular matrix and U is an upper triangular matrix, then the system Ax = b can be expressed as LUX = b and can be solved in two steps: Step 1. Let Ux = y, so that LUX = b can be expressed as Ly = b. Solve this...
5. Consider the syst em of equations: 2x-y+z2. Set up an augmented matrix and reduce to an upper triangular matrix. 5 marks a. For which value(s) of "p" (if any) does the system not have a solution? b. For which value(s) of "p" (if any) does the system have one unique solution? For which value(s) of "p" (if any) does the system have an infinite number of solutions? c. Page 5 SPRING 2019 ASSIGNMENT FILE MATH 1057 EL 12 5....
2. Solve the linear system Ax = B, by, (20P) a) Finding LU-factorization of the coefficient matrix A, b) Solving the lower triangular system Ly = b, c) Solving the upper triangular system Ux = y. where w A = 2 0 0 0 -2 1 0 2 0 0 0 0 - 1 1 1 4. -4 15 and b =
2. Consider the system: CD +2)y (t) 2x (t) a. b. c. d. Find the ZIR if y(0)-2. Find the magnitude of the frequency response. Find the phase of the frequency response. Find the steady-state solution to an input x(t)-10 cos(2t + 300)
Using MATLAB please. Recall the formula for backward substitution to solve the upper triangular system ain 011 0 012 022 bi b. alan ... 0 0 ann be which is bi - Ej=i+1 Qi; I; i= 1,...n Write a MATLAB function backward_substitution that solves an upper triangular system. Test your code using the example T 6 A 2 0 0 1 1 0 2 3 b 9 1 15
Let the LTI system be described by 3y' (t) + y(t) = 2x' (t) Find the output of this system y(t)= x(t)- hlt) for xt)= 3e 'ult).
Given the system of equations: +y+z= -6 y - 3x = 8 2x + y + 5z = – 19 (a) Determine the type of system: O dependent inconsistent (b) If your answer is dependent, find the complete solution. Write x, y, and z as functions of t, where z = t. If your answer is inconsistent, write DNE in the box for all three variables. 2= y = 2 =
(15 pts) Find (2x - y) dA, where R is the triangular region with vertices (0,0), (1, 1), and (2, -1). Use the change of variables u = x - y and v = x + 2y.
Let Is A iagonalizable? Find an upper triangular matrix B and a unitary matrix P such that B- P-1AP. Let Is A iagonalizable? Find an upper triangular matrix B and a unitary matrix P such that B- P-1AP.
4. Find the complete solution to the system 2y z t = 1 2x - y - z -t = 3 3x 2z - 2t = -2