University of Oxford mathematician Dr Tom Crawford explains how to calculate the inverse of a matrix using Elementary Row Operations (ERO’s). The video begins by explaining how matrix inverses are linked to elementary row operations via elementary matrices. The theory behind calculating the inverse for a matrix of any size is then introduced, before some worked examples on a 2×2 matrix and then a 4×4 matrix. Finally, the case of a non-invertible matrix is discussed in relation to the appearance of a zero row.

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Matrix Inverse and its Applications

Properties of the Matrix Inverses