For what value of k, does the following system of equations have a solution?x+y+z=1, x+2y+4z=k, x+4y+10z=k^2

The system of linear equations have a solution means either it can have uniques soln or infinite soln

If we go according to cramer’s rule,

here D=0

So solution can not be unique it can be infinite only

Hence D1=D2=D3 =0 will be condition. Now solve for this conditions and find values of k

That’s it!