How do we know Christ's death was for the elect?

The doctrine of limited atonement, expressed in the historic Reformed theology, teaches that Christ died specifically for the sins of the elect rather than for all humanity indiscriminately. This is supported by the narrative in Matthew 27, where the crucifixion is portrayed as fulfilling God's plan for His chosen people. Hebrews 13:12 articulates that Jesus suffered outside the camp to sanctify 'the people'—a direct reference to those God has set apart for redemption. The clear biblical assertion is that Christ's mission was not to potentially save everyone but to decisively save those whom the Father had given to Him, demonstrating the certainty and effectiveness of His sacrificial work.