System of Linear Equations
Trending Questions
Q. If the system of equations 2x+3y−z=0, x+ky−2z=0 and 2x−y+z=0 has a non-trivial solution (x, y, z), then xy+yz+zx+k is equal to :
- 34
- −4
- −14
- 12
Q. The system of equations
x+3y+2z=6x+ay+2z=7x+3y+2z=b
has
x+3y+2z=6x+ay+2z=7x+3y+2z=b
has
- a unique solution, if a=2 and b≠6
- infinitely many solutions, if a=4 and b=6
- no solution, if a=5 and b=7
- no solution, if a=3 and b=5
Q. The system of linear equations
x+y+z=2
2x+3y+2z=5
2x+3y+(a2−1)z=a+1
x+y+z=2
2x+3y+2z=5
2x+3y+(a2−1)z=a+1
- is inconsistent when |a|=√3
- has infinitely many solutions for a=4
- is incosistent when a=4
- has a unique solution for |a|=√3