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- Determine the value(s) of x so that the matrix below is the augmented matrixof an inconsistent linear system. x 1 5 5 -3 2If ? = [0 0 11 0 01 1 01 1 01 1 11 0 0101] is a parity check matrix for a linear code, then list all itscodewords.Hint: Solve the homogeneous system ? ∙ ??? = 0.6. (Linear independence ): Is it true that if x; y; and z are linearly independent vectors overGF(q), then so are x + y; y + z, and z + x ?
- Find the rank of the following matrix using determinate method. A=[1 -1 2 , -3 3 -6 , 0 1 2]If matrix A is a 2 x 3 matrix, it can be multiplie by matrix B to obtain AB only if matrix B has:A. 2 rowsB. 2 columnsC. 3 rowsD. 3 columnsIf there is a non-singular matrix P such as P-1AP=D, matrix A is called a diagonalizable matrix. A, n x n square matrix is diagonalizable if and only if matrix A has n linearly independent eigenvectors. In this case, the diagonal elements of the diagonal matrix D are the eigenvalues of the matrix A. A=({{1, -1, -1}, {1, 3, 1}, {-3, 1, -1}}) : 1 -1 -1 1 3 1 -3 1 -1 a)Write a program that calculates the eigenvalues and eigenvectors of matrix A using NumPy. b)Write the program that determines whether the D matrix is diagonal by calculating the D matrix, using NumPy. #UsePython