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Oxford Linear Algebra Rank Nullity Theorem
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=yZ52iqxaiCc
University of Oxford mathematician Dr Tom Crawford introduces the concepts of rank and nullity for a linear transformation, before going through a full step-by-step proof of the Rank Nullity Theorem. Check out ProPrep with a 30-day free trial: https://www.proprep.uk/info/TOM-Crawford • Links to the other videos mentioned: • Linear Transformations: • Oxford Linear Algebra: Linear Transfo... • Dimension Formula: • Oxford Linear Algebra: Dimension Form... • Spanning, Basis Linear Independence: • Oxford Linear Algebra: Basis, Spannin... • Subspace Test: • Oxford Linear Algebra: Subspace Test • Test your understanding of the content covered in the video with some practice exercises courtesy of ProPrep. You can download the workbooks and solutions for free here: https://api.proprep.com/course/downlo... • You can also find several video lectures from ProPrep explaining the content covered in the video here: https://www.proprep.com/courses/all/l... • As with all modules on ProPrep, each set of videos contains lectures, worked examples and full solutions to all exercises. • The video begins with the definition of the kernel and image of a linear transformation, as well as their dimensions as the nullity and rank of the linear map. Next is a fully worked example of a map in R^2 with an explicit calculation of the kernel, image, nullity and rank. • In the second part of the video the Rank Nullity Theorem is presented: the dimension of the starting vector space of a linear map is equal to the rank of the linear map (dimension of its image) plus the nullity of the map (dimension of its kernel). A full step-by-step proof is then presented by constructing a basis for each component. • Watch the 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 Easiest Method to Calculate Determinants: • Oxford Linear Algebra: The Easiest Me... • Eigenvalues and Eigenvectors Explained: • Oxford Linear Algebra: Eigenvalues an... • Spectral Theorem Proof: • Oxford Linear Algebra: Spectral Theor... • Vector Space Axioms: • Oxford Linear Algebra: What is a Vect... • Subspace Test: • Oxford Linear Algebra: Subspace Test • Basis, Spanning and Linear Independence: • Oxford Linear Algebra: Basis, Spannin... • Dimension Formula: • Oxford Linear Algebra: Dimension Form... • Direct Sum: • Oxford Linear Algebra: Direct Sum of ... • Linear Transformations: • Oxford Linear Algebra: Linear Transfo... • 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... • Check out Proprep with a 30-day free trial here: https://www.proprep.uk/info/TOM-Crawford
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