Advertisement Remove all ads

# P Investigate for What Values of 𝝁 "𝒂𝒏𝒅" 𝝀 the Equations : 2 X + 3 Y + 5 Z = 9 7 X + 3 Y − 2 Z = 8 2 X + 3 Y + λ Z = μ Have (I) No Solution (Ii) Unique Solution (Iii) Infinite Value - Applied Mathematics 1

Investigate for what values of 𝝁 "𝒂𝒏𝒅" 𝝀 the equations : 2x+3y+5z=9

7x+3y-2z=8

2x+3y+λz=μ

Have (i) no solution (ii) unique solution (iii) Infinite value

Advertisement Remove all ads

#### Solution

Given eqn :

2x+3y+5z=9

7x+3y-2z=8

2x+3y+λz=μ

  A x=B

∴ [[2,3,5],[7,3,-2],[2,3,λ]] [[x],[y],[z]] =[,,[μ]]

Argumented matrix is : [[2,3,5],[7,3,-2],[2,3,λ]][,,[μ]]

R_3-R_1

→ [[2,3,5],[7,3,-2],[0,0,λ-5]]  [,,[μ-9]]

(i) When 𝜆=5,𝝁≠𝟗 𝒕𝒉𝒆𝒏 𝒓(𝒂)= )=𝟐,𝒓(𝑨⋮𝑩)=𝟑
r(A)≠𝒓(𝑨⋮𝑩)
No Solution.
(ii) When 𝜆≠5,𝝁≠𝟗 ,𝒓(𝑨)=𝒓(𝑨⋮𝑩)=𝟑
Unique solution exist.
(iii) When 𝜆=5,𝝁=𝟗 𝒓(𝑨)=𝒓(𝑨⋮𝑩)=𝟐<𝟑
Infinite solution.

Concept: Reduction to Normal Form
Is there an error in this question or solution?
Advertisement Remove all ads

#### APPEARS IN

Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?