Use MATLAB to construct a matrix A by setting A = vander(1 : 6); A = A diag(sum(A_ )) (a) By construction, the entries in each row of A should all add up to zero. To check this, set x = ones(6, 1) and use MATLAB to compute the product Ax. The matrix A should be singular. Why? Explain. Use the MATLAB functions det and inv to compute the values of det(A) and A1. Which MATLAB function is a more reliable indicator of singularity? (b) Use MATLAB to compute det(AT ). Are the computed values of det(A) and det(AT ) equal? Another way to check if a matrix is singular is to compute its reduced row echelon form. Use MATLAB to compute the reduced row echelon forms of A and AT . (c) To see what is going wrong, it helps to know how MATLAB computes determinants. The MATLAB routine for determinants first computes a form of the LU factorization of the matrix. The determinant of the matrix L is 1, depending on whether an even or odd number of row interchanges were used in the computation. The computed value of the determinant of A is the product of the diagonal entries of U and det(L) = 1. In the special case that the original matrix has integer entries, the exact determinant should take on an integer value. So in this case MATLAB will round its decimal answer to the nearest integer. To see what is happening with our original matrix, use the

MATH 242: Elementary Differential Equations Dr. Thi Thao Phuong Hoang Notes from 8/24/17 **Note** I Anything abbreviated with is considered the first prime not to be confused with an exponent Intro 8/24/I7 Differential Equations: Functions – y :...