(Solved): If Ax=b, where A=[[1,-2,-4],[2,1,-3],[1,3,2]],x=[[x_(1)],[x_(2)],[x_(3)]] and b=[[-3],[4],[5]], dete ...

If

, where

and

, determine: a) determinant of

. (3 marks) b) if

is singular or non-singular? (1 mark) c) the rank of

and of

and hence determine the nature of the solution. (3 marks) d)

(6 marks) e) the solution for the set of equations using the answer obtained in part d). (3 marks) II) Determine the eigenvalues and corresponding eigenvectors of

(10 marks)