What will be the minimum number of multiplication to multiply these matrices?
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subject : analysis of
Q.No.1: Consider the following chain of matrices having matrices A, B, C and D. You have to consider the digits of your Registration Number in the order of the matrix as given. Add 2 to the digit if its zero.
For example, your Reg_No. 19-Arid-797 has last digit 7, 2nd last digit 9 and 3rd last digit 7.
A B C
2 X last digit last digit X 2nd last digit 2nd last digit X 3nd last digit
D
3rd Last digit X 4
What will be the minimum number of multiplication to multiply these matrices? Show the order of multiplication as well.
Step by step
Solved in 2 steps
- This question is about the Matrix Chain Multiplication problem. You are given four matrices with the following dimensions.Write 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.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]
- 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…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)?. The determinant of an n X n matrix can be used in solving systems of linear equations, as well as for other purposes. The determinant of A can be defined in terms of minors and cofactors. The minor of element aj is the determinant of the (n – 1) X (n – 1) matrix obtained from A by crossing out the elements in row i and column j; denote this minor by Mj. The cofactor of element aj, denoted by Cj. is defined by Cy = (-1y**Mg The determinant of A is computed by multiplying all the elements in some fixed row of A by their respective cofactors and summing the results. For example, if the first row is used, then the determi- nant of A is given by Σ (α(CI) k=1 Write a program that, when given n and the entries in an n Xn array A as input, computes the deter- minant of A. Use a recursive algorithm.
- Determined the eigenvalues of the matrix (A) given below? A=[1 0 4; 0 4 0; 3 5 -3]The join of two zero-one matrices A and B is described as AvB = [aij v bij] AAB = [aij a bij] AAB = [aij v bij] AvB = [aij a bij]In matlab can you please show me a code that can output the given matrices? use matrix operation :D any code except for this one "K = [4 3 2 1;5 14 13 12;6 15 16 11;7 8 9 10]"
- List any two properties of eigenvalues of a square matrix. Explain it in your own way and provide it with examples.Find the product of the elements of a matrix by other elements of a matrix with integer random elements and the size of each (4 x 2) of them.Find Matrix Chain multiplication for following four matrices (M1, M2, M3 and M4) using dynamic programming Technique.