Linear Algebra
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Linear Algebra

Part 7 : Inverses and Gauss-Jordan Elimination

Inverse of a matrix

Inverse of Matrix A
Identity matrix has same order
Order doesn’t matter when a matrix is multiplied with its inverse

Matrix Division

Resulting matrix

Gauss-Jordan Elimination

Carl Friedrich Gauss
Wilhelm Jordan
Matrix A
Identity matrix for matrix A
Augmented matrix of matrix A and I
Elements eliminated from first column
Row echelon form
Second row is reduced
Reduced Row Echelon Form
Inverse of matrix A

Are all matrices invertible?

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