X+ y + w = b
2x + 3y + z + 5w = 6
z + w = 4
2y + 2z + aw = 1
for what values a, b (constants) is the system:
(a) inconsistent?
(b) consistent w/ a unique sol'n?
(c) consistent w/ infinitely-many sol'ns?

(a) a=6 and b≠

(b)a≠6

(c) a=6 and b=

Step-by-step explanation:

writing equation in agumented matrix form

now

now

a) now for inconsistent

rank of augamented matrix ≠ rank of matrix

for that  a=6 and b≠

b) for consistent w/ a unique solution

rank of augamented matrix = rank of matrix

  a≠6

c) consistent w/ infinitely-many sol'ns

  rank of augamented matrix = rank of matrix < no. of variable

for that condition

 a=6 and b=[tex]\frac{11}{4}

then rank become 3 which is less than variable which is 4.

3/6   and 9/18

step-by-step explanation: