Question

Suppose we have a system of equations AX = B, where A is the coefficient matrix
and C = [A[B] is the augmented matrix. Then the given system of equations will
consistent if
(a) rank(A) = rank(C)
(c) rank(A) = 0 & rank(C) = 1
(b) rank(A) # rank(C)
(d) none​

Answer 1

Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.