Question

Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. -6 15 h 2 -5 4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The matrix is the augmented matrix of a consistent linear system if h = (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) OB. The matrix is the augmented matrix of a consistent linear system if h# . (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) O C. The matrix is the augmented matrix of a consistent linear system for every value of h. D. The matrix is not the augmented matrix of a consistent linear system for any value of h.

Answer 1

Given Augumented Matrix is ch. - 6 IS [A16] 2 4 R12 2 -S 4 h -6 Rx+3R, 2 S O O ht 12 This is eachton form of Tow FA1-B1 system of linear Equation AX-B is consistent -Rank [AB] Rank[A] only when Here Rank (A) = al Rank (AIB) -and =1 (from only for he-12 Hence The of matrix is the Augmented matrix 9 consistent linear system if th = -12 -Option is correct.