Question

14. Find the values of a and b for which the system of equations
x + y + z = 3,
x + 2 y + 2 z = 6,
x + a y + 3 z= b
have
(i) no solution;
(ii) unique solution; and
(iii) more than one solution.
15.

Answer 1

Step-by-step explanation:

Step-by-step explanation:If the system of equations has no solution then

Step-by-step explanation:If the system of equations has no solution then Δ=0 and at least one of Δ

Step-by-step explanation:If the system of equations has no solution then Δ=0 and at least one of Δ 1

Step-by-step explanation:If the system of equations has no solution then Δ=0 and at least one of Δ 1

Step-by-step explanation:If the system of equations has no solution then Δ=0 and at least one of Δ 1 ,Δ

Step-by-step explanation:If the system of equations has no solution then Δ=0 and at least one of Δ 1 ,Δ 2

Step-by-step explanation:If the system of equations has no solution then Δ=0 and at least one of Δ 1 ,Δ 2

Step-by-step explanation:If the system of equations has no solution then Δ=0 and at least one of Δ 1 ,Δ 2 and Δ

Step-by-step explanation:If the system of equations has no solution then Δ=0 and at least one of Δ 1 ,Δ 2 and Δ 3

Step-by-step explanation:If the system of equations has no solution then Δ=0 and at least one of Δ 1 ,Δ 2 and Δ 3

Step-by-step explanation:If the system of equations has no solution then Δ=0 and at least one of Δ 1 ,Δ 2 and Δ 3 is not zero.

Step-by-step explanation:If the system of equations has no solution then Δ=0 and at least one of Δ 1 ,Δ 2 and Δ 3 is not zero.Δ=

Step-by-step explanation:If the system of equations has no solution then Δ=0 and at least one of Δ 1 ,Δ 2 and Δ 3 is not zero.Δ= ∣

Step-by-step explanation:If the system of equations has no solution then Δ=0 and at least one of Δ 1 ,Δ 2 and Δ 3 is not zero.Δ= ∣∣

Step-by-step explanation:If the system of equations has no solution then Δ=0 and at least one of Δ 1 ,Δ 2 and Δ 3 is not zero.Δ= ∣∣∣

l

1

11

111

111

111

111

111

111 a

111 a2

111 a25

111 a25

111 a25

111 a25

111 a25

111 a25 1

111 a25 12

111 a25 123

111 a25 123

111 a25 123

111 a25 123 ∣

111 a25 123 ∣∣

111 a25 123 ∣∣∣

111 a25 123 ∣∣∣∣

111 a25 123 ∣∣∣∣∣

111 a25 123 ∣∣∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 =

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 1

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 11

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 1

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 12

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 3

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b ∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b ∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b ∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b ∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b ∣∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b ∣∣∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b ∣∣∣∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b ∣∣∣∣∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b ∣∣∣∣∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b ∣∣∣∣∣∣∣∣

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b ∣∣∣∣∣∣∣∣ 

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b ∣∣∣∣∣∣∣∣ =0

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b ∣∣∣∣∣∣∣∣ =0⟹b

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b ∣∣∣∣∣∣∣∣ =0⟹b

111 a25 123 ∣∣∣∣∣∣∣∣ =0⟹−a−1=0⟹a=−1Δ 2 = ∣∣∣∣∣∣∣∣ 111 123 36b ∣∣∣∣∣∣∣∣ =0⟹b=9