4. F(n) = 1 n=1 3 F(2^) +2, n>1
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- Let L₁ = {aa, bb}, L₂ = {A, a, aa}, L3 = {x | x = {a,b}* ^ |x| ≤ 3} = {A, a, b, aa, ab, ba, bb, aaa, aab, aba, abb, baa, bab, bba, bbb}. Evaluate: (L₁n L3) · L2 = •Python numpy library functions to perform basic matrix operations are as follows.• C=numpy.add(A, B): Add two matrices A and B and store result in C.• C=numpy.subtract(A, B): Subtract matrix B from matrix A and store result in C.• C=numpy.divide(A, B): Divide matrix A by matrix B and store result in C.• C=numpy.multiply(A, B): Multiply matrix A by matrix B and store result in C.• C=numpy.sum(A): Form the sum of elements of matrix A and store result in c ∈ R.• C=numpy.sum(A, axis = 0): Form the column wise summation of matrix A andstore result in vector C.• C=numpy.sum(A, axis = 1): Form the row wise summation of matrix A, storeresult in vector C.Python code to show the implementation of these methods in a sample matrix.Given the following definitions: U={a,b,c, d, e, f, g} A={a, c, e, g} B={a,b,c,d} find A n B
- Solution Floating point representation: It is defined as the representation of floating numbers. It includes sign bit, exponent, and mantissa bits. Based on precision it has 2 types. 1. For IEEE 754 single-precision floating-point numbers, what is the exponent of a denormalized floating-point number in decimal? Solution: In IEEE 754 single-precision, exponent bits are 8. Therefore exponent = 2 ^(n-1) -1 = 2^(8-1) -1 = 127 OPTION D 2. For IEEE 754 single-precision floating-point numbers, how many bits for mantissa? Solution: In IEEE 754 single-precision, there are 23 bits for mantissa. sign = 1 bit exponent = 8 bits mantissa = 23 bits 3. For IEEE 754 single-precision floating-point numbers, which of the following is an example of NAN? Solution: In IEEE 754 single-precision, NAN is a special value where all exponents bits are 1's and the mantissa is non zero. a. 1 111 1 111 0000 0000 1101 0000 0000 0000 Exponent is not all 1's. Not a NAN b. 0 111 1 111 1000 0000…In c programming without pointer and function Problem Statement A matrix is a 2D array of numbers arranged in rows and columns. We give you a Matrix of N rows and M columns. Now your task is to do this operation on this matrix: If the value matches with the current row and column number then add 3 with the value. If the value matches with only the current row number then add 2 with the value. If the value matches with only the current column number then add 1 with the value. Input Format The first line contains N is the number of rows in this matrix and M is the number of columns in this matrix The second line contains a 2D array Arr[i][j]. Constraints 1 <= N, M <= 10 0 <= Arr[i][j] <= 100 Output Format Print the matrix after the operation is done. Sample Input 0 3 31 1 11 1 11 1 1 Sample Output 0 4 3 3 2 1 1 2 1 1A = [1 1; 1 -1];b = [80; 20]; A_inverse = inv(A);x = A\b; disp('A inverse is');disp(A_inverse);disp(['x1 is ', num2str(x(1)), ' and x2 is ', num2str(x(2))]); if isequal(round(x), [50; 30]) disp('Success');else disp('Incorrect: Please try again');end. Output matlab. .
- 2: Which code is considered correct to use for matrix multiplication using dot product method? > a=[1,2,3;4,5,6]; >b=[0,1,7;3,2,1]r; » a=[1,2,3,4,5,6]; »b=[0,1,7;3,2,1]; >>d=a.*b; »d=a*b; Code 2 Code 3 > a=[1,2,3;4,5,6]; »b=[0,1,7,3,2,1); > a=[1,2,3;4,5,6]; »b=[0,1,7;3,2,1); »d=a*b; >d=a.*b; Code 4 Code 1convert c code to mips these 2 functions are linked with each other. #define MAX_BOARD_SIZE 12 // Players #define PLAYER_EMPTY 0 #define PLAYER_BLACK 1 #define PLAYER_WHITE 2 int board_size; int current_player = PLAYER_BLACK; char board[MAX_BOARD_SIZE][MAX_BOARD_SIZE]; int main(void); void announce_winner(void); unsigned int count_discs(int player); void announce_winner(void) { int black_count = count_discs(PLAYER_BLACK); int white_count = count_discs(PLAYER_WHITE); if (white_count > black_count) { printf("The game is a win for WHITE!\n"); white_count += count_discs(PLAYER_EMPTY); } else if (black_count > white_count) { printf("The game is a win for BLACK!\n"); black_count += count_discs(PLAYER_EMPTY); } else { printf("The game is a tie! Wow!\n"); } printf("Score for black: %d, for white: %d.\n", black_count, white_count); } unsigned int count_discs(int player) { int count = 0; for (int row = 0; row < board_size; ++row) { for (int col = 0; col < board_size; ++col) { if…Python problem Problem statementDevelop a program that receives a matrix and determines whether it corresponds to a magic square. A magic square is one that the sum of its elements in each of the rows is equal to the sum of the elements in each of the columns and also equal to the sum of the elements of each of the diagonals. The condition that the numbers from 1 to n ** 2 are used must also be met, where n is the size of the magic square, which is a matrix of nxn. https://upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Magicsquareexample.svg/1200px-Magicsquareexample.svg.png EntryThe first line corresponds to the number n. After this, n lines, each line contains a list of integers separated by a space. DepartureIf the square is magic, it must print the value that has the sum of the numbers by columns, rows and main diagonals. If it is not a magic square, the word "Error" must be printed without quotation marks. Examples Input Example 1 416 3 2 135 10 11 89 6 7 124 15 14 1Output…
- typedef struct { short data[4];} MatrixElement; void copy_matrix(MatrixElement m1[], MatrixElement m2[], int ROWS, int COLS) { int i, j, k; for (i = 0; i < ROWS; i++) { for (j = 0; j < COLS; j++) { for (k = 0; k < 4; k++) { m1[i*COLS+j].data[k] = m2[i*COLS+j].data[k]; } } }} void copy_matrix_transpose(MatrixElement m1[], MatrixElement m2[], int ROWS, int COLS) { int i, j, k; for (i = 0; i < ROWS; i++) { for (j = 0; j < COLS; j++) { for (k = 0; k < 4; k++) { m1[i*COLS+j].data[k] = m2[j*ROWS+i].data[k]; } } }} You can assume the following conditions: The matrix m1 is allocated at memory address 0, and matrix m2 immediately follows it. Indices i, j, and k are kept in registers. ROWS and COLS are constants. The cache is initially empty before the function call. The cache is write-back (i.e., only writes back to memory when a line is…16. Get the sum of all the values in matrix In [ ]: In [28]: # DON'T WRITE HERE Out[28]: 1275 17. Get the standard deviation of the values in matrix In [29]: # Code Here In [30]: # DON'T WRITE HERE Out[30]: 14.430869689661812Use C Language The Pascal triangle can be used to compute the coefficients of the terms in the expansion (a + b)n. For example, (a + b)2 = a2 + 2ab + b2 where 1, 2, and 1 are coefficients. Write a C program that creates a two-dimensional matrix a representing the Pascal triangle of size n. For example, a Pascal triangle of size 6 is shown below: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1