Home
Class 12
MATHS
Consider the system of linear equations:...

Consider the system of linear equations:
`x_(1) + 2x_(2) + x_(3) = 3`
`2x_(1) + 3x_(2) + x_(3) = 3`
`3x_(1) + 5x_(2) + 2x_(3) = 1`
The system has

A

no solution

B

infinite number of solutions

C

exactly three solutions.

D

a unique solution

Text Solution

Verified by Experts

The correct Answer is:
1
`Delta = |{:(1,,2,,1),(2,,3,,1),(3,,5,,2):}|=0, Delta_(1)= |{:(3,,2,,1),(3,,3,,1),(1,,5,,1):}|ne 0`
hence the given system does not have any solution .
Promotional Banner

Similar Questions

Explore conceptually related problems

The system of linear equations x_(1)+2x_(2)+x_(3)=3, 2x_(1)+3x_(2)+x_(3)=3 and 3x_(1)+5x_(2)+2x_(3)=1 , has

Let lambda in R . The system of linear equations 2x_(1) - 4x_(2) + lambda x_(3) = 1 x_(1) -6x_(2) + x_(3) = 2 lambda x_(1) - 10x_(2) + 4 x_(3) = 3 is inconsistent for :

Consider the system of linear equations; x-1\ +2x_2+x_3=3 2x_1+3x_2+_3=3 3x_1+5x_2+2x_3=1 The system has Infinite number of solutions Exactly 3 solutions A unique solution No solution

If the system of linear equations x_(1)+2x_(2)+3x_(3)=6,x_(1)+3x_(2)+5x_(3)=9,2x_(1)+5x_(2)+ax_(3)=b, is consistent and has infinite number of solutions,then :-

The system of linear equations x + y + z = 2 2x + 3y + 2z = 5 2x + 3y + (a^(2) - 1)z = a + 1

The system of linear equations x+y+z =2, 2x+3y+2z = 5 2x +3y+ (a^(2)-1)z = a + 1