Kernel Perceptron for inseparable data query

Any clues as to the following would be appreciated.

For inseparable data the Perceptron algorithm will go into an infinite loop.

Assuming the training examples are distinct, consider the modification of

a normalised kernel k to

**k**(x; z) = *k*(x; z) + a.*g*(x; z);

where a > 0 and

*g*(x; z) =

1 if x = z;

0 otherwise:

Show we can find a such that *K*.a = y for the label vector y, where *K* is

the kernel matrix of the modied kernel *k*. Hence, argue that the training

set is separable in the feature space defined by the kenel mapping phi(x).