How do we know that faith is essential for healing according to Matthew?

In the narrative found in Matthew 15, we see that the Canaanite woman approached Jesus with a firm belief that He had the power to heal her daughter. Jesus acknowledges her faith by stating, 'O woman, great is thy faith; be unto thee even as thou wilt' (Matthew 15:28). This interaction underscores that faith is not merely an abstract concept but plays an active role in obtaining God's blessings, including physical healing. Moreover, throughout the Gospels, instances of healing are frequently accompanied by the declaration of faith, reinforcing the biblical principle that faith is the channel through which God's power operates in our lives. It also illustrates that even those considered outsiders can possess genuine faith and receive God's grace.