13. + . Solve: 2. Suppose: 21 = 2+1, 2=3–21, and 23=- (a) 321 +421 (b) +-3 +421-8
QUESTION 19 21 Evaluate the finite geometric series : 2 2(3/5)"-1 n=1 21 -50 14.9 4.99
15. Prove that for all n 21 and r 2 1, +2 Tl n +1 15. Prove that for all n 21 and r 2 1, +2 Tl n +1
2. For the following signal x(t), find and sketch x(1-2), x(1+2),x(-1), X(21) and -2x(3-21). X(t) Note: You must indicate the function for each segment.
Y13) = re-1+21)22 42(2) = zel-1-21)22 Write the solution yı (2) as a sum of real and imaginary parts, y(I) = u(x) +iv(x), where u(2) and v(r) are real-valued. Based on the information given, are u(I) and v(2) solutions to the differential equation Briefly justify your answer.
(1) Simplify the following expressions as much as possible. c) (-1+1)2(1)(i(21+1)+δ(-21+1)] (Draw also the resulting function for part (c))
1 1 -21 2. Problem 2 Let A= -1 2 1 0 1 -1/ (a) (1 point) Find the eigenvalues and eigenvectors of A. Solution: vastam 2 101 - 60: (b) (1 point) Find the eigenvectors of A. Solution: (c) (1 point) Find an invertible matrix P such that P-AP = D, where D is a diagonal matrix. Solution:
Question 2 Find the general solution to 21 2 -2 X1 X2 1 4 32 Enter Answer D Question 3 Find the solution to the initial value problem X1 1 -2 21 2] [3 (2:0) = [] X1(0) 22(0) X2 3 6 X2 Enter Answer Question 2 Find the general solution to 21 2 -2 X1 X2 1 4 32 Enter Answer D Question 3 Find the solution to the initial value problem X1 1 -2 21 2] [3 (2:0)...
T67 [21] (1 point) Let A = 1 1 and b = [21] -6 .The QR factorization of the matrix A is given by: 1-3] [21] [ 11 = [2 1 112] 2 -V2 ماده و V2 (a) Applying the QR factorization to solving the least squares problem Ax = b gives the system: (b) Use backsubstitution to solve the system in part (a) and find the least squares solution. 5/3 -3
Find the general solution to 2 -2 21 [es] 1 4 32