Verified Certificate

Supported by the following organizations

This is to certify that William Ray Lucas successfully completed and received a passing grade in UT.5.05x: LAFF: Linear Algebra - Foundations to Frontiers a course of study offered by UTAustinX, an online learning initiative of University of Texas System.

Noted by

Steven Mintz

Steven Mintz

Executive Director, Institute for Transformational Learning The University of Texas System

James W. Pennebaker

James W. Pennebaker

Executive Director of Project 2021 and Regents Centennial Professor of Psychology The University of Texas at Austin

Dr. Robert van de Geijn

Dr. Robert van de Geijn

Professor of Computer Science The University of Texas at Austin

Dr. Maggie Myers

Dr. Maggie Myers

Lecturer The University of Texas at Austin

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