Exercises 1. Why is BTBL (see above for definitions) a diagonal matrix? 2 The determinant of a matrix A is equal to the product of the eigenvalues. Write a code that uses only the eig command and basic operations (such as multiplication and addition to compute the determinant of the matrix A= [ 2 -1 0 -1 2-1 0 -1 2]; You can check your answer by using MATLAB's det command. As usual, find out how to use the det command by using the help command. 3. Compute the eigenvalues of the 1000x1000 matrix 1 2 -1 Li 2 A= 0 -1 0 ... -1 0... 2 -1 0 0 0 0 -1 0 2 -1 -1 2 Exercises 1. Why is BTBL (see above for definitions) a diagonal matrix? 2 The determinant of a matrix A is equal to the product of the eigenvalues. Write a code that uses only the eig command and basic operations (such as multiplication and addition to compute the determinant of the matrix A= [ 2 -1 0 -1 2-1 0 -1 2]; You can check your answer by using MATLAB's det command. As usual, find out how to use the det command by using the help command. 3. Compute the eigenvalues of the 1000x1000 matrix 1 2 -1 Li 2 A= 0 -1 0 ... -1 0... 2 -1 0 0 0 0 -1 0 2 -1 -1 2