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Problem X. Take the method for finding the inverse of a given n x n matrix A -a by straightforwar...
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...
7. Let A [aij] be an n x n invertible tridiagonal matrix, that is aij= 0 if |i - j > 1. Compute the number of operations needed to solve the system Ax b by Gauss elimination without partial pivoting. (10 marks)
7. Let A [aij] be an n x n invertible tridiagonal matrix, that is aij= 0 if |i - j > 1. Compute the number of operations needed to solve the system Ax b by Gauss elimination without...
PROBLEM 3 (20%) Evaluate the following determinants: PROBLEM-i120%) Given the matrix 3 3 1 (a Fin...
help me solve problem 4,5 & 6
PROBLEM 3 (20%) Evaluate the following determinants: PROBLEM-i120%) Given the matrix 3 3 1 (a FindAby applying Gauss-Jordan elimination 3400 -3 2 5 2 -2I 1 500 0-2 3600-3 7 -700 1-2 (b) Find by applying determinant and matrix adjoint formula PROBLEM 5110961 Let Ade 2. evaluate 3a -3b -3c (b) ICId e f (c) IDIbeh (d)IE (e) 13A [ABC! IDEI PROBLEM 6 120%) Find a way to linearise the following equations, and...
(a) Suppose we want to solve the linear vector-matrix equation Ax b for the vector x. Show that the Gauss elimination algorithm may be written bAbm,B where m 1, This process produces a matrix equa...
(a) Suppose we want to solve the linear vector-matrix equation Ax b for the vector x. Show that the Gauss elimination algorithm may be written bAbm,B where m 1, This process produces a matrix equation of the form Ux = g , in which matrix U is an upper-triangular matrix. Show that the solution vector x may be obtained by a back-substitution algorithm, in the form Jekel (b) Iterative methods for solving Ax-b work by splitting matrix A into two...
2. (a) Let A be the matrix A -4 21 8 -40 Write down the 3 x 3 permutation matrix P such that PA interchanges the 1st and 3rd rows of A. Find the inverse of P. Use Gaussian elimination with partial pi...
2. (a) Let A be the matrix A -4 21 8 -40 Write down the 3 x 3 permutation matrix P such that PA interchanges the 1st and 3rd rows of A. Find the inverse of P. Use Gaussian elimination with partial pivoting to find an upper triangular matrix U, permutation matrices Pi and P2 and lower triangular matrices Mi and M2 of the form 1 0 0 Mi-1A1 10 a2 0 1 M2 0 0 0 b1 with ail...
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.
4. Suppose that A Rnn is nonsingular. We can pose the problem of finding A-1 as...
4. Suppose that A Rnn is nonsingular. We can pose the problem of finding A-1 as the system of linear equations where X e R" is the unknown inverse matrix. We assume that A has LU factorization A LU (a) Explain how we can use the LU factorization of A and the ear system (4.1.1) to calculate the inverse A-1 Hint: The system (4.1.1) is a system of n × n equations and n × n unknowns. Consider the linear...
Problem 2.2 n and let X ε Rnxp be a full-rank matrix, and Assume p Note that H is a square n × n ...
Please show all work in READ-ABLE way. Thank you so much in
advance.
Problem 2.2 n and let X ε Rnxp be a full-rank matrix, and Assume p Note that H is a square n × n matrix. This problem is devoted to understanding the properties H Any matrix that satisfies conditions in (a) is an orthogonal projection matriz. In this problem, we will verify this directly for the H given in (1). Let V - Im(X). (b) Show that...
7. Let A [aij] be an n x n invertible tridiagonal matrix, that is aij= 0 if |i - j > 1. Compute the number of operations needed to solve the system Ax b by Gauss elimination without partial pivoting. (10 marks)
7. Let A [aij] be an n x n invertible tridiagonal matrix, that is aij= 0 if |i - j > 1. Compute the number of operations needed to solve the system Ax b by Gauss elimination without...
help me solve problem 4,5 & 6
PROBLEM 3 (20%) Evaluate the following determinants: PROBLEM-i120%) Given the matrix 3 3 1 (a FindAby applying Gauss-Jordan elimination 3400 -3 2 5 2 -2I 1 500 0-2 3600-3 7 -700 1-2 (b) Find by applying determinant and matrix adjoint formula PROBLEM 5110961 Let Ade 2. evaluate 3a -3b -3c (b) ICId e f (c) IDIbeh (d)IE (e) 13A [ABC! IDEI PROBLEM 6 120%) Find a way to linearise the following equations, and...
(a) Suppose we want to solve the linear vector-matrix equation Ax b for the vector x. Show that the Gauss elimination algorithm may be written bAbm,B where m 1, This process produces a matrix equation of the form Ux = g , in which matrix U is an upper-triangular matrix. Show that the solution vector x may be obtained by a back-substitution algorithm, in the form Jekel (b) Iterative methods for solving Ax-b work by splitting matrix A into two...
2. (a) Let A be the matrix A -4 21 8 -40 Write down the 3 x 3 permutation matrix P such that PA interchanges the 1st and 3rd rows of A. Find the inverse of P. Use Gaussian elimination with partial pivoting to find an upper triangular matrix U, permutation matrices Pi and P2 and lower triangular matrices Mi and M2 of the form 1 0 0 Mi-1A1 10 a2 0 1 M2 0 0 0 b1 with ail...
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.
4. Suppose that A Rnn is nonsingular. We can pose the problem of finding A-1 as the system of linear equations where X e R" is the unknown inverse matrix. We assume that A has LU factorization A LU (a) Explain how we can use the LU factorization of A and the ear system (4.1.1) to calculate the inverse A-1 Hint: The system (4.1.1) is a system of n × n equations and n × n unknowns. Consider the linear...
Please show all work in READ-ABLE way. Thank you so much in
advance.
Problem 2.2 n and let X ε Rnxp be a full-rank matrix, and Assume p Note that H is a square n × n matrix. This problem is devoted to understanding the properties H Any matrix that satisfies conditions in (a) is an orthogonal projection matriz. In this problem, we will verify this directly for the H given in (1). Let V - Im(X). (b) Show that...
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