What is the trace of a matrix? a. The sum of the diagonal elements. b. The product of the diagonal elements. c. The sum of all elements. d. The difference of the diagonal elements.

What is the trace of a matrix? Calculate the trace of a 3x3 identity matrix

Let R=⎛⎝x000y000z⎞⎠ be a non-zero 3×3 matrix, where xsinθ=ysin(θ+2π3)=zsin(θ+4π3) ≠0,θ∈(0,2π). For a square matrix M, let trace (M) denote the sum of all the diagonal entries of M. Then, among the statements:(I) Trace (R)=0(II) If trace (adj(adj(R))=0, then R has exactly one non-zero entry.

What is the main diagonal of a matrix?a.The elements from the top left to the bottom rightb.The elements from the edges to the middlec.The elements from the middle to the edgesd.The elements from the top right to the bottom left

Write a program to obtain a matrix and find the sum of its diagonal elements.Note: Only square matrix.Input format :The input consists of the number of rows and columns separated by a space.The second line of the input is matrix elements.Output format :The output prints the sum of diagonal elements.Refer to the sample input and output for format specifications.Sample test cases :Input 1 :3 31 2 34 5 67 8 9Output 1 :15Input 2 :4 412 23 45 5678 89 98 8765 54 32 2114 25 36 58Output 2 :191

Find the elements of the diagonal and the lower elements.Write a program to obtain a matrix and find the sum of the elements in the lower triangular matrix.Note: Only square matrixInput format :The first line of the input consists of the number of rows and columns.The second line of the input consists of the matrix element.Output format :The output prints the sum of the lower triangular matrix.Refer to the sample input and output for format specifications.Sample test cases :Input 1 :3 312 23 4556 78 8995 51 20Output 1 :312