2. Describe the dynamics of the linear maps whose matrix is given below. Identify precisely the s...
Explanation and graphs are important here
8. Describe the dynamics of a linear map F: R-R, F(z)= Az, z E R2, whose matrix representation is 1/2 0 -2 0 a) A = 0 2 0 1 2 :) =ra (5)-
8. Describe the dynamics of a linear map F: R-R, F(z)= Az, z E R2, whose matrix representation is 1/2 0 -2 0 a) A = 0 2 0 1 2 :) =ra (5)-
on # 3) For the below given system find if the system is: a. Linear or Non-Linear b. Time variant or Time invariant c. Memory or Memory less d. Causal or Non-causal e. Stable or unstable System is given by y(t) -etx(t)
Find the general solution of the system whose augmented matrix is given below. 2 -5 - 20 20 0 -15 15 0 Choose the correct answer below OA O B. O C. O D. The system has no solutions. x-2x2 5 5 x25x3 <x2=-5 X is free X is froo 3=5 x is free
Find the general solution of the system whose augmented matrix is given below. 2 -5 - 20 20 0 -15 15 0 Choose the correct answer...
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
10.10 If A is an 'n x n matrix, and x is an n x 1 vector, then the linear transformation y = Ar maps* n to·m, so the linear transformation should have a condition number, condAx (x). Assume that l a subordinate norm a. Show that we can define condar (x)-[All Irl/IArll for every x 0. b. Find the condition number of the linear transformation atx [ - 2 using the oo-norm ng the oo-norm. T-3 2 1 .12...
of the linear system whose augmented matrix is the matrix (b) Find all solutions (in vector form ſi 0-5 -6 0 77 B = 0 1 4 -1 0 2 . 0 0 0 0 1 -3
2. For the linear time-invariant systems with impulse responses given below, determin if the system is BIBO stable or BIBO unstable. (a) h)--21-3)lu)-u(t-5)] (b) h(t)--for t > 2 and h(t) = 0 for t < 2 (c) h(t)-cos tu(t) (d) h(t) coste 'u(t) t -1
Consider the linear transformation T: "R" whose matrix A relative to the standard basis is given. A=[1:2] (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) (11, 12) = 2,3 |_) (b) Find a basis for each of the corresponding eigenspaces. B = X B2 = = {I (c) Find the matrix A' for T relative to the basis B', where B'is made up of the basis vectors found in part (b). A=
With explanation!
3. Let B2 be the linear operator B2f (x):- f(0)2 2 (1f (1)2, which maps functions f defined at 0, 1 to the quadratic polynomials Pa. This is the Bernstein operator of degree 2, Let T = B21Py be the restriction of B2 to the quadratics. (a) Find the matrix representation of T with respect to the basis B = [1,2,2 (b) Find the matrix representation of T with respect to the basis C = (1-x)2, 22(1-2),X2]. (c)...