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Oxford Linear Algebra: The Easiest Method to Calculate Determinants

University of Oxford mathematician Dr Tom Crawford explains how to calculate the determinant of a matrix using ERO’s, with a worked example for a 4x4 matrix. Check out ProPrep with a 30-day free trial to see how it can help you to improve your performance in STEM-based subjects: https://www.proprep.uk/info/TOM-Crawford Test your understanding with some practice exercises courtesy of ProPrep. You can download the workbooks and solutions for free at the links below. Elementary Row Operations: https://www.proprep.uk/Academic/Downl... Determinants: https://www.proprep.uk/Academic/Downl... You can also find fully worked video solutions from ProPrep instructors at the links below. 4x4 matrices: https://www.proprep.uk/general-module... 5x5 matrices: https://www.proprep.uk/general-module... Watch other videos from the Oxford Linear Algebra series at the links below. Solving Systems of Linear Equations using Elementary Row Operations (ERO’s):    • Oxford Linear Algebra: Elementary Row...   Calculating the inverse of 2x2, 3x3 and 4x4 matrices:    • Oxford Linear Algebra: How to find a ...   What is the Determinant Function:    • Oxford Linear Algebra: What is the De...   The video begins with a recap of the determinant function introduced in the previous video. The three types of elementary row operations are also revisited. Next, we see how applying any ERO to a matrix is equivalent to pre-multiplying the matrix by an elementary matrix - which is just the identity with the desired ERO applied to it. Using the multiplicative property of the determinant, det(AB) = det(A)det(B), the effect of an elementary row operation on the determinant is reduced to multiplying by the determinant of an elementary matrix. The determinant of each type of elementary matrix is calculated and thus a summary of how each ERO affects the determinant is provided. Finally, a fully worked example of calculating the determinant of a 4x4 matrix using ERO’s is shown. 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...