1- If x= [1 4; 8 3], find: a) the inverse matrix of x. b) the diagonal of x. c) the sum of each column and the sum of whole matrix x. d) the transpose of x.
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- Exercises2 1- If x=[1 4; 8 3], find :Using matlab a) the inverse matrix of x. b) the diagonal of x. c) the sum of each column and the sum of whole matrix x. d) the transpose of x. 2- If x= [2 8 5; 9 7 1], b=[2 4 5] find: a) find the maximum and minimum of x. b) add the vector b as a third row to x.Exercises 1- If x=[1 4; 8 3], find: a) the inverse matrix of x. b) the diagonal of x. c) the sum of each column and the sum of whole matrix x. d) the transpose of x.The command (find) is -:used to O O find the maximum number within a matrix find the minimum number within a matrix extract the numbers satisfying a condition evaluate the average of a group of numbers determine the locations of numbers satisfying a condition O O
- construct a Playfair matrix with the key "largest"Write a program that fills a 5 x 5 matrix with the following data: Upper left triangle with -1 Lower right triangle with 1 Right to left diagonal with 0O B The method in which matrix rows are selected and multiply the corresponding cofactors to yield determinant is called (A) Three factor expansion (B) Cofactor expansion (C) One factor expansion (C) Cofactor expansion and minor O A
- Linear Equation SystemLU Decomposition Method AlgorithmDecomposition phase The LU Decomposition (Doolittle) method has the following properties: The U matrix is identical to the upper triangular matrix resulting from the Gaussian Elimination;The elements at the bottom below the main diagonal of the matrix L are the multipliers used during the Gaussian Elimination, that is, Li*j is the multiplier that eliminated Ai*j.It is common practice to store the multipliers at the bottom of the coefficient matrix, replacing the coefficients as they are eliminated (Li*j replacing Ai*j) The diagonal elements of L do not need to be stored, as their values are understood to be unitary. The final form of the coefficient matrix would be the mixture of L and U: The initial part of the LU Decomposition Method algorithm is identified with Gaussian Elimination, except that each λ multiplier is now stored in the lower triangular portion of matrix A: solve the system of linear equations followed by the…# Function to find sum of all # sub-squares of size k x k in a given # square matrix of size n xn def sum_sub_squares (matrix, k): n = len(matrix) result = [[0 for i in range(k)] for j in range(k)] if k>n: return for i in range(n - k + 1): 1=0 for j in range(n-k+ 1): sum = 0 # Calculate and print sum of current sub-square for p in range(i, k + i): for q in range(j, k+j): sum += matrix[p][q] result[i][1] = sumNine coins are placed in a 3-by-3 matrix with someface up and some face down. You can represent the state of the coins using a3-by-3 matrix with values 0 (heads) and 1 (tails). Here are some examples:0 0 0 1 0 1 1 1 0 1 0 1 1 0 00 1 0 0 0 1 1 0 0 1 1 0 1 1 10 0 0 1 0 0 0 0 1 1 0 0 1 1 0Each state can also be represented using a binary number. For example, the precedingmatrices correspond to the numbers000010000 101001100 110100001 101110100 100111110There are a total of 512 possibilities, so you can use decimal numbers 0, 1, 2,3, . . . , and 511 to represent all states of the matrix. Write a program that promptsthe user to enter a number between 0 and 511 and displays the correspondingmatrix with the characters H and T. Here is a sample run: Enter a number between 0 and 511: 7 ↵EnterH H HH H HT T T The user entered 7, which corresponds to 000000111. Since 0 stands for H and1 for T, the output is correct.
- Q3: Consider the scores of 12 students in Computer course (X) and Mathematic course (Y) given as follows: 1 2 3 4 5 6 7 8 9 10 11 12 74 70 20 74 90 73 55 97 72 68 51 80 Y 80 91 33 73 99 73 67 93 88 70 74 86 Answer the following questions by writing the suitable Matlab statements: 1) to create a matrix named A of 2 lines and 12 columns, the first line of this matrix contains the scores of students in Computer course, the second line contains the scores of students in Mathematic course. 2) to find the score average of the fifth student using the matrix A. 3) to find the most frequent score of Mathematic course using the matrix A. 4) to find the first and third quartiles of Computer course using the matrix A.Matlab screenshot - If x=[ 2 6 12; 15 6 3; 10 11 1], then a) replace the first row elements of matrix x with its average value. b) reshape this matrix into row vector.python # Initialize a 6x6 matrix with all elements as 0 matrix = [[0 for _ in range(6)] for _ in range(6)] # Fill in the matrix for i in range(6): # Iterate over rows for j in range(6): # Iterate over columns if i > j: matrix[i][j] = 3*j - 4*i else: matrix[i][j] = 0 # Print the matrix for row in matrix: print(row)