Given any non-homogenous system of linear equation (n*n), the system will have a unique solution (non-trivial) if and only if the determinant of its coefficient matrix is non-zero. On the other hand the system will have infinitely many solutions if its determinant equal to zero. A conjugate transpose of matrix A A 1 inverse of square matrix A(if it exists) I n n nunit matrix 0 n n nzero matrix AB matrix product of m nmatrix A and n pmatrix B jk Kronecker delta with jk= 1 for j= k and jk= 0 for j6= k eigenvalue real parameter t time variable H Hamilton function L Lagrange function
Dec 07, 2012 · 850 as a solution, and setting c= 1 yields 941 as another solution. C51 (Robert Beezer) Find all of the six-digit numbers in which the rst digit is one less than the second, the third digit is half the second, the fourth digit is three times the third and the last two digits form a
(i) There is no solution if h – 1 = 0 and 5 – k is not zero, so no solution if h = 1 and k is not 5. (ii) There is a unique solution if h – 1 is not zero and 5 – k is any real number, so a unique solution exists if h is not 1 and k is any real number. (iii) For the system to have many solutions, there would have to be a free variable.