Homogeneous System of Equations
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Q. Consider the planes
P1:cy+bz=x
P2:az+cx=y
P3:bx+ay=z.
P1, P2 and P3 pass through one line, if
P1:cy+bz=x
P2:az+cx=y
P3:bx+ay=z.
P1, P2 and P3 pass through one line, if
- a2+b2+c2=ab+bc+ca
- a2+b2+c2+2abc=1
- a2+b2+c2=1
- a2+b2+c2+2ab+2bc+2ca+2abc=1
Q. Find tbe sum of all the values of λ for which the system of equations λx+y+z=1, x+λy+z=λ, x+y+λz=λ2 has infinite number of solutions.
Q. Let λ be a real number for which the system of linear equations
x+y+z=6
4x+λy−λz=λ−2
3x+2y−4z=−5
has infinitely many solutions. Then λ is a root of the quadratic equation :
x+y+z=6
4x+λy−λz=λ−2
3x+2y−4z=−5
has infinitely many solutions. Then λ is a root of the quadratic equation :
- λ2+3λ−4=0
- λ2−3λ−4=0
- λ2+λ−6=0
- λ2−λ−6=0