M L Aggarwal Solutions for Chapter: Determinants, Exercise 6: EXERCISE 4.6

Which of the following equations are consistent? If consistent, solve them.

$x-y+3z=6$

$x+3y-3z=-4$

$5x+3y+3z=14$.

Which of the following equations are consistent? If consistent, solve them.

$4x-2y+6z=8$

$2x-y+3z=4$

$2x-y+3z=13$.

Which of the following equations are consistent? If consistent, solve them.

$2x+y+3z=4$

$x-2y+z=-2$

$5x-5y+z=-2$.

Which of the following systems has non-trivial solutions? If so, find these solutions.

$5x+5y+2z=0$

$2x+5y+4z=0$

$4x+5y+2z=0$.

Which of the following systems has non-trivial solutions? If so, find these solutions.

$2x-3y-z=0$

$x+3y-2z=0$

$x-3y=0$.

If the system of equations is $x-ky-z=0, kx-y-z=0,x+y-z=0$ has a non-zero solution, then find the possible values of $k$.

Find the real value(s) of a for which the system of equations

$x+ax=0,y+az=0,z+ax=0$

has infinitely many solutions.

If the equations $x=cy+bz,y=az+ex,z=bx+ay$ are consistent, prove that $a^2+b^2+c^2+2abc=1.$