6.1.1.c. LU Decomposition Method

Try these first

1. 1.

   Define LU Decomposition.

   Hint

   Think about how we can break down a matrix.

2. 2.

   What are the two types of matrices involved in LU Decomposition?

   Hint

   Think of the shapes of the matrices.

3. 3.

   What does LU Decomposition do?

   • Factors a matrix into its singular values
   • Decomposes a matrix into lower and upper matrices
   • Solves the matrix using determinants

   Hint

   Think of what LU Decomposition breaks a matrix into.

4. 4.

   True or False: LU Decomposition can only be applied to square matrices.

   • True
   • False

   Hint

   Consider the shape of matrices that can be decomposed.

5. 5.

   Consider the matrix A = [[a, b], [c, d]]. Propose how one might approach LU Decomposition for this general case.

   Hint

   Use the properties of lower and upper triangular matrices.

6. 6.

   Given the system of equations represented by a matrix A, identify how changing a single element can affect the LU Decomposition.

   Hint

   Think about how dependent the matrices are on their initial elements.