I can't find answer to a problem. The problem is like this:
Find the basis for where is a linear transformation.
Part of Solution:
The problem is solved like this:
The reduced row echelon form of augmented matrix is:
So the solutions are:
How do you find the basis for now because ?
But you are still going to get the same thing: T(x, y, z)= (x+ 2y, y+ 2z, z+ 2x)= (0, 0, 0). That is, we must have x+ 2y= 0, y+ 2z= 0, and z+ 2x= 0. From the first equation, x= -2y. From the second, y= -2z so x= -2(-2z)= 4z. But from the third equation z= -2x so that x= 4(-2x)= -8x which is only satified for x= 0. Then z= -2x= 0 and y= -2z= 0. The entire kernel is the single 0 vector. That does not have a basis.
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HallsofIvy Thanks again.