Consider the following training dataset with input X$=($x$1,$ x$2)$ and target $($desired$)$ output d$.$ A neuron with two inputs and one output is used for this training dataset. Activation function is a linear function with zero bias. Sum of square error is used as the loss function.

A$.$ If back propagation is used, what will be the weights $($w$1,$ w$2)$ after convergence?

B$.$ What will be the nature of the loss function? What is the value of learning rate which leads to convergence in least number of iterations? Show all calculation steps.

C$.$ To achieve convergence in least number of iterations, will you use batch gradient descent, stochastic gradient descent or mini batch gradient and why?