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My trouble is finding the bais for the kernel of the linear map

L: R4 -> R1 defined by L([a,b,c,d)]=a-b-2c+d

I know the dimension of the kernel is 3, but how?

I have tried setting it against the standard basis and that's not right.

I tried solving it by using four vectors with different values, and that keeps giving me a linear dependent vector.

PLEASE HELP!!!

Am I missing something? I can row reduce and pull out the constants, but I have no idea how to get to the matrix.