MathAlgebraLinear algebraMatrix decomposition

LU Decomposition

Step-by-step matrix L

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Sort the given steps below to create a step-by-step plan for calculating the lower triangle matrix $L$ of a matrix $A$ .

Put the items in the correct order

Instantiate

L

as the identity matrix with the same size as

A

Continue this process for each step of Gaussian Elimination until you have filled in all positions below the main diagonal of

L

Recall the previously applied Gaussian Elimination used to obtain

U

. Store the multipliers used for eliminating entries below the main diagonal in the corresponding position of

L

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