wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If S is the set of distinct values of ' b' for which the following system of linear equations
x+y+z=1x+ay+z=1ax+by+z=0
has no solution, then S is


A

an infinite set

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

a finite set containing two or more elements

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

a singleton set

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

an empty set

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

a singleton set


Explanation for the correct option.

Step 1: Find the value of a

For the system of equations with no solution, the determinant of the coefficient matrix should be 0

1111a1ab1=0

On solving the determinant we get:
1(a-b)-1(1-a)+1b-a2=0a-b-1+a+b-a2=02a-1-a2=0-(a-1)2=0a=1
Step 2: Find the value of b

For a=1, the equations become:
x+y+z=1x+y+z=1x+by+z=0
From the above three equations, we can see that if b=1, the system will be inconsistent and hence will produce no solution.

For b1, the system will produce infinite solutions.
So, S has to be a singleton set {1} for no solution.

Hence, option C is correct.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
What's Your Capacity?
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon