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7. Let A [aij] be an n x n invertible tridiagonal matrix, that is aij= 0 if |i - j > 1. Compute the number of operat...
a e Octave a a Caleculator to qn i. Calculate the number N equal to the sum of all digits of your SID ii. For the N × N matrix A = (aij) defined as aij-l if i = j, or i + 1 = j, and aij 0 for all oth...
a e Octave a a Caleculator to qn i. Calculate the number N equal to the sum of all digits of your SID ii. For the N × N matrix A = (aij) defined as aij-l if i = j, or i + 1 = j, and aij 0 for all other values of (i,j) Compute (A-)x for x ,,1 ER . Compute (A-1)Tx for x = [1, 2, 3, . . . , NIT E RN. . Compute x-A(A-19%...
Let A-(Aij)i iJSn є {0,1)"xn denote the symmetric adjacency matrix of an undi- rected graph. For iメj, we have Aij = 1 if entity i and j are connected in a network and 0 otherwise: A 0, i-1,...,...
Let A-(Aij)i iJSn є {0,1)"xn denote the symmetric adjacency matrix of an undi- rected graph. For iメj, we have Aij = 1 if entity i and j are connected in a network and 0 otherwise: A 0, i-1,..., n. The stochastic block model (SBM) postulates where is a full rank symmetric K x K connectivity matrix with entries in [0, 1]. a) Consider the matrix P-M MT, where M {0,1)"xK denotes the community k-1,... , K. Show that under (1),...
Problem X. Take the method for finding the inverse of a given n x n matrix A -a by straightforwar...
Problem X. Take the method for finding the inverse of a given n x n matrix A -a by straightforward Gauss (or Jordan) elimination (Problem 7 is a particular case for n 3). First you write down the augmented matrix A and apply the Gauss process to this as discussed in class: A-la2,1 a2,2 a2,n : an,1 an,2 .. an.n 0 0 1 3. Derive the Jordan elimination algorithm without pivoting for the augmented matrix in terms of a triple...
8. Let An be the following n x n tridiagonal matrix ab 0 0 0 Cab...
8. Let An be the following n x n tridiagonal matrix ab 0 0 0 Cab 00 0 0 Oca 0 0 0. 0 0 0 C a Show that AnalAn- 1l-bc|A,-21 for n 2 3. If a = 1+bc, show that |An 1+bc+ (be)2 ++(bc)" If a 2 cos with 0 <0<T and b c 1 then show that sin (n+1)0 |An = sin 0 nn change
8. Let An be the following n x n tridiagonal matrix ab...
a) Let I be the n x n identity matrix and let O be the n × n zero matrix
a) Let I be the n x n identity matrix and let O be the n × n zero matrix . Suppose A is an n × n matrix such that A3 = 0. Show that I + A is invertible and that (I + A)-1 = I – A+ A2. b) Let B and C be n x n matrices. Assume that the product BC is invertible. Show that B and C are both invertible.
Problem 2 Let A be an n x n matrix which is not 0 but A-0...
Problem 2 Let A be an n x n matrix which is not 0 but A-0 Let I be the identity matrix. a) (10 Points) Show that A is not diagonalizable. b) (5 Points) Show that A is not invertible. e) (5 Points) Show that I-A is invertible and find its inverse.
For the following problems use: Annx n matrix A is invertible RREF(A) = I rank(A) - n A 2 x 2 matrix A is invertible =...
For the following problems use: Annx n matrix A is invertible RREF(A) = I rank(A) - n A 2 x 2 matrix A is invertible = det(A) 0 3 singular (non-invertible). For which value(s) of h is A = -2 -1 -4 Choose... Choose... 6 2 h-2 a 0,b 0,c+0,d +0 A = 4 -1 C 0 x-2 or x 4 For which values of x is A = invertible a 0,b 0,c 0,d=0 4 x 2 X#1 and x2...
Q1 The linear system Ax = b is given by: x1−x2 + 4x3 = 7 4x1...
Q1 The linear system Ax = b is given by: x1−x2 + 4x3 = 7 4x1 + 2x2 –x3= 18, x1 + 3x2+ x3 = 16, has the solution x=(3, 4,2)T. Using the initial guess x (0)=(1, 1,1)T Solve the above system as is using: Gauss-Seidel method. If the error increases, what does that mean and what should you do? (see b below) Condition the system so that convergence is secured and solve using the Gauss-Siedel method. Q2: Find a system...
1. [A] is the coefficient matrix for [Aj[X]-(C. 12-10 16 A-16 9 24 12 8 At the end of forward elimination steps of Gaussian Elimination method with partial pivoting, the coefficient matrix looks...
1. [A] is the coefficient matrix for [Aj[X]-(C. 12-10 16 A-16 9 24 12 8 At the end of forward elimination steps of Gaussian Elimination method with partial pivoting, the coefficient matrix looks like 0 0 by a) bs is most nearly (circle correct response) [10 pts.] A. -2.0298 B. 1.4167 C. 12.000 D. 22.667 b) This is a consistent/inconsistent system. (circle correct response) (5 points) A square matrix [A] is upper triangular if (circle correct response) |5 points (A)...
a e Octave a a Caleculator to qn i. Calculate the number N equal to the sum of all digits of your SID ii. For the N × N matrix A = (aij) defined as aij-l if i = j, or i + 1 = j, and aij 0 for all other values of (i,j) Compute (A-)x for x ,,1 ER . Compute (A-1)Tx for x = [1, 2, 3, . . . , NIT E RN. . Compute x-A(A-19%...
Let A-(Aij)i iJSn є {0,1)"xn denote the symmetric adjacency matrix of an undi- rected graph. For iメj, we have Aij = 1 if entity i and j are connected in a network and 0 otherwise: A 0, i-1,..., n. The stochastic block model (SBM) postulates where is a full rank symmetric K x K connectivity matrix with entries in [0, 1]. a) Consider the matrix P-M MT, where M {0,1)"xK denotes the community k-1,... , K. Show that under (1),...
Problem X. Take the method for finding the inverse of a given n x n matrix A -a by straightforward Gauss (or Jordan) elimination (Problem 7 is a particular case for n 3). First you write down the augmented matrix A and apply the Gauss process to this as discussed in class: A-la2,1 a2,2 a2,n : an,1 an,2 .. an.n 0 0 1 3. Derive the Jordan elimination algorithm without pivoting for the augmented matrix in terms of a triple...
8. Let An be the following n x n tridiagonal matrix ab 0 0 0 Cab 00 0 0 Oca 0 0 0. 0 0 0 C a Show that AnalAn- 1l-bc|A,-21 for n 2 3. If a = 1+bc, show that |An 1+bc+ (be)2 ++(bc)" If a 2 cos with 0 <0<T and b c 1 then show that sin (n+1)0 |An = sin 0 nn change
8. Let An be the following n x n tridiagonal matrix ab...
a) Let I be the n x n identity matrix and let O be the n × n zero matrix . Suppose A is an n × n matrix such that A3 = 0. Show that I + A is invertible and that (I + A)-1 = I – A+ A2. b) Let B and C be n x n matrices. Assume that the product BC is invertible. Show that B and C are both invertible.
Problem 2 Let A be an n x n matrix which is not 0 but A-0 Let I be the identity matrix. a) (10 Points) Show that A is not diagonalizable. b) (5 Points) Show that A is not invertible. e) (5 Points) Show that I-A is invertible and find its inverse.
For the following problems use: Annx n matrix A is invertible RREF(A) = I rank(A) - n A 2 x 2 matrix A is invertible = det(A) 0 3 singular (non-invertible). For which value(s) of h is A = -2 -1 -4 Choose... Choose... 6 2 h-2 a 0,b 0,c+0,d +0 A = 4 -1 C 0 x-2 or x 4 For which values of x is A = invertible a 0,b 0,c 0,d=0 4 x 2 X#1 and x2...
1. [A] is the coefficient matrix for [Aj[X]-(C. 12-10 16 A-16 9 24 12 8 At the end of forward elimination steps of Gaussian Elimination method with partial pivoting, the coefficient matrix looks like 0 0 by a) bs is most nearly (circle correct response) [10 pts.] A. -2.0298 B. 1.4167 C. 12.000 D. 22.667 b) This is a consistent/inconsistent system. (circle correct response) (5 points) A square matrix [A] is upper triangular if (circle correct response) |5 points (A)...
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