If A and B are rectangular matrices as the following: A = (ay)pxq and B = (bij)nxm and AB = BA, then n=q=m=p (q=n) and (mp) m=p q=n (q=m) and (n = p)
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- The meet of two zero-one matrices A and B is described as AAB = [ajj A bj] AvB = [aj A bijl] A v B = [aj v bijl A AB = [aj v bijl]Given A = {1,2,3} and B={u,v}, determine. a. A X B b. B X BWrite the functions that will calculate the trace and the determinant of the matrices. The trace of the matric is defined as the sum of the diagonal elements, i.e., Tr = ₁ aii. The standard formula to find the determinant of a 3 x 3 matrix is to a break it down into smaller 2 x 2 determinants Mij, known as minors, det The minor Mij is defined to be the determinant of the (n-1) x (n-1) matrix that results from A by removing the i-th row and the j-th column. The minors would be determinants of the 2 × 2 matrices, which could be easliy calculated from the formula n (A)=(-1)+c j=1 b deta d C ¡Mij. aij = ad bc.
- A What is the product of matrices M=(1,0)(0,-3) and N=(0,1)(0,-3)? B What is the difference of matrices M=(1,0,2)(0,-3,1) and N=(0,1,2)(0,0,-3)? C What is the a(3) term of the sequence {a(n)} where a(n) = 2n - 6? 1.D What is the range of a function that assigns to a 16-bit bit string the number of one bits in the bit string? E What is the sum of matrices M=(1,0,2)(0,-3,1) and N=(0,1,2)(0,0,-3)? F If f(x) = 2x + 3, find f(S) if S={0,2,5}. G What is the transpose of matrix M=(1,0,2)(0,-3,1)?You have to run Prim's algorithm for the problem defined by adjacency matrix: 1 2 3 4 5 6 7 8 9 1 0 10 9 999 999 17 999 999 999 2 3 69 10 0 14 4 2 999 999 13 999 14 0 7 999 999 999 999 999 4 999 4 7 0 999 2 8 999 999 5 999 2 999 999 0 6 999 1 999 6 17 999 999 2 6 0 999 7 999 7 999 999 999 8 999 999 0 11 4 8 999 13 999 999 1 7 11 9 999 999 999 999 999 999 4 80 8 0 1. We started from the vertex vl, so initially we have Y = {v1}: initial 1 2 3 4 5 6 7 8 9 nearest 1 1 1 1 1 1 1 1 1 distance -1 10 9 999 999 17 999 999 999 Print out the values stored in the nearest and distance arrays after first iteration of Prim's algorithm. Specify the value of vnear and the next vertex that has to be added to Y Hint: use (copy) the table above to record your answer.läs 5 Find the SUM for mean of the matrix * ? F F= 1 1 1 1 2 2 2 2 3 3 3 4 4 4 4 sum(mean (F)) O sum (sum F) O mean(mean(F)) O Jalbo läl li 3.
- 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…Solving Equations Using Matrix Perform the following Matrix Operations for the predefined matrices. Given the System of equations: 2х + 4у—5z + Зw %3D — 33 Зх + 5у-2г + бw %3D —37 x- 2y + 4z – 2w = 25 Зх + 5у—3г + Зw %3D - 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. Find the Eigenvalues of A. 5. Form the Reduced Row Echelon of A. 6. Find the number of rows and number of columns of Ab. 7. Find the sum of the columns of A. 8. In each of the columns of A, find the highest values and its indices. 9. Augment A with b; 10. Determine the Rank of Ab 11. Find blA 12. Form the Reduced Row Echelon of Ab. 13. Extract the Last Column of the Reduced Row Echelon Form of Ab. 14. Create a matrixA whose elements are the same as matrix A, but the first column is the column vector b. 15. Create a matrix A whose elements are the same as…suppose a computer solves a 100x100 matrix using Gauss elimination with partial pivoting in 1 second, how long will it take to solve a 300x300 matrix using Gauss elimination with partial pivoting on the same computer? and if you have a limit of 100 seconds to solve a matrix of size (N x N) using Gauss elimination with partial pivoting, what is the largest N can you do? show all the steps of the solution
- If A = {1, 2, 6} and B = {2, 3, 5}, then the union of A and B isQ3: Find the eigenvalues of the Matrix: C = 3 21 1 ادة / صباحي : انور عدنان یحییUSING PYTHON A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal (i.e., ai,j where j = i) and the ones immediately above and belowit(i.e.,ai,j wherej=i+1orj=i−1). Write a function that solves a linear system whose coefficient matrix is tridiag- onal. In this case, Gauss elimination can be made much more efficient because most elements are already zero and don’t need to be modified or added. Please show steps and explain.