Matrix A has dimension m x n and Matrix B has dimension s x t. Design conditions for m, n, s and t so that both matrix products AB and BA are defined.
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Matrix A has dimension m x n and Matrix B has dimension s x t. Design conditions for m, n,
s and t so that both matrix products AB and BA are defined.
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- Perform the following Matrix Operations for the predefined matrices. Given the System of equations: 2х + 4y — 5z + Зw %3D —33 3х + 5у—2z + бw %3D — 37 х — 2у + 4z — 2w 3 25 Зх + 5у-3z + Зw = -28 Write the systems as Ax = b, where A is the coefficient matrix and b is the vector for the constants. 1. Encode the Matrix A and the column vector b. 2. Solve for Determinant of A. 3. Find the Inverse of A. 4. Form the Reduced Row Echelon of A. 5. Find the number of rows and number of columns of Ab. 6. Find the sum of the columns of A. 7. In each of the columns of A, find the highest values and its indices. 8. Augment A with b; 9. Find b\A 10. Form the Reduced Row Echelon of Ab. 11. Extract the Last Column of the Reduced Row Echelon Form of Ab. 12. Create a matrix A whose elements are the same as matrix A, but the first column is the column vector b. 13. Create a matrix A whose elements are the same as matrix A, but the second column is the column vector b. 14. Create a matrix A whose elements…(a) Suppose we want to change columns 6 and 7 in our matrix A. Express the new matrix as A - ZVT, where Z and V have dimension n × 2. (b) Suppose we want to change both column 6 and row 4 of A. Find Z and V so that our new matrix is A - ZVT.H.W Find the Adjoint to the following matrix Z =-1 5 4 3 -2
- Problem 1: Write a general Gauss Elimination (GE) code 1) Use the left-hand side matrix and right-hand side vector we provide to test your code. Output your solution. 2) Randomly generate matrix A and b with N = 100, 1000, and 10000 to test your code.6. Using the root vectors, work out the weight diagram of 10.2. Matrix Quantum Mechanics. Use python matrix and algebraic tools for this problem. Consider orthogonal vectors [1], [2) and [3). The operators C and P are represented by C = /C₁ 00 0 C₂ 0 0 0 C3. /P₁ 0 0 P = 0 0 P2 0 P3 Where all quantities are real. a) Do the operators C and P commute? b) Find the eigenvalues and normalized eigenvectors of the given operators.
- Use a simple algorithm to do the following ant it as a matlab code 1. Determine the mean of the elements of a matrix A WITHOUT using the mean function 2. Find out how many non-zero elements a matrix A has 3. Sum the diagonal elements of a square matrix A 4. Add the first and last elements of a vector v if you are not given the length of vH.W Find the Adjoint to the following matrix -2 3- Y = 1 4 1 -3Draw the following graph as represented in the adjacency matrix below. a b c d A 1 1 1 0 B 0 1 1 0 C 0 0 1 1 d 0 0 0 1