Which of the following is not equivalent to the nxn matrix a being invertible? a. the homogeneous system associated to a has a unique solution. b. some non-homogeneous system whose coefficient matrix is a has a unique solution. c. every non-homogeneous system whose coefficient matrix is a is consistent. d. the column space of a is r". e. the linear transformation x h ax is one-to-one.

Option C

Step-by-step explanation:

       AB = 0, B =

      Thus, B = (0, 0, 0......., 0) is a unique solution

     2. The non - homogeneous equation system with coefficient matrix A has  a unique solution:

For an equation- AY = D

Y = is a unique solution

     3. Every non homogeneous equation with coefficient matrix A is not consistent as:

For an equation- AY = D, has a solution.l Thus coefficient matrix is inconsistent whereas augmented matrix is.

      4. Rank of matrix A = n, Thus the column space of A is

      5. Since, column space of A = , thus x→xA is one-to-one

use this formula:

p(a\b) = p(a and b)/p(b).

take it from here.

the answer is c

hope this !