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Oxford Linear Algebra: Elementary Row Operations (EROs) Explained

University of Oxford mathematician Dr Tom Crawford explains how to solve a system of linear equations using matrices and elementary row operations (EROs). Check out ProPrep with a 2-week free trial to see how it can help you to improve your performance in STEM subjects: https://www.proprep.uk/ Test yourself with some practice exercises courtesy of ProPrep. You can download the workbooks and solutions for free at the links below. Algebraic Equations: https://www.proprep.uk/Academic/Downl... Systems of Linear Equations: https://www.proprep.uk/Academic/Downl... You can also find fully worked video solutions courtesy of ProPrep instructors at the links below. Systems of Two Linear Equations: https://www.proprep.uk/general-module... Linear Systems - Zero or Infinite Systems: https://www.proprep.uk/general-module... Systems of Linear Equations: https://www.proprep.uk/general-module... SLE with Parameter: https://www.proprep.uk/general-module... The video begins by solving a system of 3 equations with 3 unknowns using the methods of substitution and elimination. The same system is then converted into a matrix equation and the concept of elementary row operations (EROs) is introduced. The 3 types of ERO are explained and then used to reduce the coefficient matrix to the identity, allowing the solution to be deduced. Two further cases are discussed through worked examples - a zero row with a zero entry in the solution vector, and a zero row with a non-zero entry in the solution vector. In the first case we see how the system is underdetermined with infinitely many solutions, whilst in the second case the system is inconsistent and therefore has no solutions. Finally, a summary of everything discussed is presented at the end of the video. Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: https://www.seh.ox.ac.uk/people/tom-c... For more maths content check out Tom's website https://tomrocksmaths.com/ You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.   / tomrocksmaths     / tomrocksmaths     / tomrocksmaths   Get your Tom Rocks Maths merchandise here: https://beautifulequations.net/collec...