The given problem solve Using matrix inversion.
Question 5 15 pts Consider the following matrices: 2 -21 3 0 9 A= -1 1...
Activity 15 - Matrices, Sequences and Conics Math 180 Task 6: Matrices and Cryptography messages. Using the following code, Matrices are used to encode and decode encrypted KİLİMİN 2 | 3 | 4 | 5 | 6 17 18 T-9 10111 | 12 | 13 | 14 一0一ㄧ一Pー1_Qー1.RT-s-T_T-I-U 15 16 17 18 19 20 21 ㄨㄧㄒㄧㄚ 1-2.TSPACE 24 25 26 ˇ一ㄒ一w 22 23 The sentence MATRICES ARE FUN becomes: AİRİE 13 1 20 189 3 5 19 0 1 18...
3) (9 points) For each of the following matrices Find the eigenvalues and associated eigenvectors. If possible, state the matrices P and D, such that A = PDP-1. (Hint: P is a matrix containing eigenvectors of A on its columns, and D is a diagonal matrix.) If it is not possible to find P and D, just state so. 11-133b a. A = 1 2 2 1-2 -2 -2 2 0 -1 3] b. A = [1 -4 110 0...
Consider the following matrices: 1 2 A= 3-4 2 3 B= 3 2 1 1 0 2 C= 2 1 3 -1 1 1 1 4 5 -4 2 5 1 3 4 1 0 1 1 - 2 D= E= F 4 1 31 7 3 2 Find each of the following, if possible. If it is not possible, explain your reasoning. 1 (a) AB (9) BAT (b) BA (h) (A + B) E (C) CD + E ()...
5. Let B be the following matrix in reduced row-echelon form: 1 B= 1 -1 0-1 0 0 2 0 0 0 0 0 0 0 0 (a) (3 pts) Let C be a matrix with rref(C) = B. Find a basis of ker(C). (b) (3 pts) Find two matrices A1 and A2 so that rref(A1) = rref(A2) im(A) # im(A2). B, and 1 (c) (5 pts) Find the matrix A with the following properties: rref(A) = B, is an...
Question 5. (20 pts.) a)Find Eigenvalues and Eigenvectors of the following matrix 3 2 6 1 -2 3 L6 4 12 b) Find the Fourier series representation of the function with period 21 given by t2 0 <t<TE i < t < 270 f(t) = {.
Question 5 9 marks Consider a Markov chain {YTheN with state space S = {1,2,3,4), initial distribution Po (0.25,0.25, 0.5,0), and transition matrix 1/3 2/3 0 0 p 1/6 1/2 1/30 0 4/9 4/9 1/9 0 0 5/6 1/6 2(a) Find the equilibrium probability distribution T (b) Find the probability P(-1%-3. Ya-1). Question 5 9 marks Consider a Markov chain {YTheN with state space S = {1,2,3,4), initial distribution Po (0.25,0.25, 0.5,0), and transition matrix 1/3 2/3 0 0 p...
(4) (15 marks) Repeat the Question 2 for the following matrices -3 4 0] 0 0 A -2 30 B 0 -1 0 -8 8 1 0 0 1 ū= 10 = > 3 (I) (2 mark) Find the characteristic polynomial of matrix A. (II) (1 mark) Find eigenvalues of the matrix A. III) (2 mark) Find a basis for the eigenspaces of matrix A. IV) (1 mark) What is the algebraic and geometric multiplicities of its eigenvalues. (V) (2...
7. (15 pts) For the matrix A= -3 1 2 3 6 -2 - 4 -9 -1 1-7 2 3 -1 5 8 - 4 4 9 0 a) Use your calculator to place the matrix in RREF. b) Find a basis for the Range(A). c) Find a basis for Nul(A).
7. Consider the following matrices 2 3-1 0 1 A=101-2 3 0 0 0-1 2 4 2 3 -1 B-101-2 0 0-1 2 3 -1 0 c=101-2 3 For each matrix, determine (a) The rank. (b) The number of free variables in the solution to the homogeneous system of equa- tions (c) A basis for the column space d) A basis for the null space for matrices A and HB e) Dimension of the column space (f) Nullity (g) Does...
1. On Inverting Matrices, using Gauss-Jordan (a) Consider the following matrix A. If the inverse of A exists, com- pute A-1, else say so. A 1 3 INVERSE OF MATRICES 15 (b) Consider the following matrix A. If the inverse of A exists, com- pute A-1, else say so. A-(3) 0 1 (c) Consider the following matrix A. If the inverse of A exists, com- pute A1, else say so. 0 2 (d) Consider the following matrix A. If the...