Write a Matlab function for a matrix that takes
in a matrix in echelon form and will return the row
canonical form. The function cannot use
rref, or any other matlab built in functions.
11.
Given a row echelon form or the reduced row echelon form of an
augmented matrix of a system of equations, determine the number of
solutions the system has.
1. For both systems below form the augmented matrix, reduce
the augmented matrix to echelon form
(zeros below the diagonal), and give the solution to the
system.
(a) x – 2y + z = 0; 2x + 3y – z = 16; 3x – y – 3z = 23.
(b) 2x – 3y + z = -3; x + 2y – 5z = -29; 3x – y + 2z =
-2
The following matrix is in reduced row echelon form. Decode from
the matrix the solution of the corresponding system of linear
equations or state that the system is inconsistent. (If the system
is dependent assign the free variable the parameter t. If
the system is inconsistent, enter INCONSISTENT.)
1
0
5
−4
0
1
−8
10
0
0
0
0
(x1, x2,
x3) =
Give an example of an augmented matrix in echelon form
corresponding to a system of 2 equations in three unknowns
satisfying each of the following conditions or explain why it is
not possible.
(a) No solutions
(b) One unique solution
(c) Infinitely many solutions.