1) Let A be nxn matrix and Ax=b, if we need change A to Upper triangular...

1) Let A be nxn matrix and Ax=b, if we need change A to Upper triangular matrix using Gaussian Elimination, how many additions/subtraction operations are involved? how many multiplication/division operations are involved?

2) Once we got the upper triangular matrix, now we need to apply back-substitution, how many additions/subtraction operations are involved? how many multiplication/division operations are involved?

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Let Un×n be an upper triangular matrix of rank n. If any arithmetic operation takes 1µ...

Let Un×n be an upper triangular matrix of rank n. If any arithmetic operation takes 1µ second on a computing resource, compute the time taken to solve the system Ux = b, assuming it has a unique solution. What would be the time taken if Un×n is lower triangular

Let A be an m x n matrix. Prove that Ax = b has at least...

Let A be an m x n matrix. Prove that Ax = b has at least one solution for any b if and only if A has linearly independent rows. Let V be a vector space with dimension 3, and let V = span(u, v, w). Prove that u, v, w are linearly independent (in other words, you are being asked to show that u, v, w form a basis for V)

et A be a 157 x 157 upper-triangular matrix. Suppose that every diagonal entry of A...

et A be a 157 x 157 upper-triangular matrix. Suppose that every diagonal entry of A is 1 and that there is at least one nonzero off-diagonal entry in A. Is A diagonalizable? Explain how you can answer this question mentally, with no non-trivial calculations.

MATLAB Function: (Backward substitution) Write a function that takes an upper triangular matrix U, and a...

MATLAB Function: (Backward substitution) Write a function that takes an upper triangular matrix U, and a vector b as input and returns the solution of the linear system U x = b. Use this function in the case when U is made of the numbers [(3,2,1),(0,5,4),(0,0,6)], and b = [1,1,−6]^T.

for matrices, what is the difference between row reduced echelon form and an upper triangular matrix?

1. Let ??(F), ??(F) and ??(F) denote the spaces of strictly upper triangular, diagonal, and strictly...

1. Let ??(F), ??(F) and ??(F) denote the spaces of strictly upper triangular, diagonal, and strictly lower triangular ?×? matrices over F, respectively. Show that ??(F) = ??(F)⊕??(F)⊕??(F). Compute the dimensions of these spaces and show they sum 2 up to ?. 2. Is the set {?3 +2?2,−?2 +3?+1,?3 −?2 +2?−1} in P3(R) linearly independent? Is it a basis?

Suppose the system AX = B is consistent and A is a 6x3 matrix. Suppose the...

Suppose the system AX = B is consistent and A is a 6x3 matrix. Suppose the maximum number of linearly independent rows in A is 3. Discuss: Is the solution of the system unique?

3. Let P be an nxn projection matrix (which means that it satisfies P2=P and PT=P)....

3. Let P be an nxn projection matrix (which means that it satisfies P2=P and PT=P). The goal of this problem is to show that P as a linear transformation is the orthogonal projection onto the range of P. (a) Show that if v is in the range of P, then Pv=v. (b) Show that if v is orthogonal to the range of P then Pv=0. (Hint: PPv lies in the range of P, hence is orthogonal to v. Study...

Matrix: Ax b [2 1 0 0 0 | 100] [1 1 -1 0 -1 |...

Matrix: Ax b [2 1 0 0 0 | 100] [1 1 -1 0 -1 | 0] [-1 0 1 0 1 | 50] [0 -1 0 1 1 | 120] [0 1 1 -1 1 | 0] Problem 5 Compute the solution to the original system of equations by transforming y into x, i.e., compute x = inv(U)y. Solution: %code I have not Idea how to do this. Please HELP!

A linear system of equations Ax=b is known, where A is a matrix of m by...

A linear system of equations Ax=b is known, where A is a matrix of m by n size, and the column vectors of A are linearly independent of each other. Please answer the following questions based on this assumption, please explain all questions, thank you~. (1) Please explain why this system has at most one solution. (2) To give an example, Ax=b is no solution. (3) According to the previous question, what kind of inference can be made to the...

Subjects