Photonic Tensor Cores (PTCs) have been raised as one of the major candidates to accelerate Neural Network hardware, taking advantage of the high bandwidth, low latency, and energy efficiency that propagating light has over the electrical counterpart. However, actual solutions still rely on external bulk components, such as lasers, modulators, and photodetectors. In this work, we show the first fully integrated hybrid Silicon Photonics PTC for computing Matrix-Vector Multiplication (MVM), one of the main steps for any Neural Network layer. The PTC is formed by a WDM 3-fold InP laser array connected to an active Silicon Photonic PIC through Photonic Wire Bondings. The CW lasers are modulated by high-speed Mach-Zehnder modulators to generate the input vector. The mix of all the signals is sent into a 3x3 matrix, formed by highspeed add-drop coupled microring resonators, whose tuning signals are the weights of the matrix. Outputs are collected by a bank of high-speed integrated photodetectors. The whole photonics IC has a footprint of 4.1×1.7 mm 2 , including lasers, allowing to have just electrical I/O. The full integration of input modulators, weights, and photodetectors can allow the PIC to work at over 20 GHz bandwidth with extremely low latency. This integration is a key step toward the actual deployment of photonics as an NN-accelerator for future AI systems.