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# Knowledge Base

## Solution 11726: Computing the Doolittle LU (lower-upper) Decomposition of a Matrix on the TI-89 Family, TI-92 Family, and Voyage™ 200 Graphing Calculators.

### How do I compute the LU decomposition of a matrix on the TI-89 family, TI-92 family, or Voyage 200 graphing calculator?

The instructions below demonstrate how to compute the Doolittle (lower-upper) decomposition of a real or complex matrix on the TI-89 family, the TI-92 family, and Voyage 200.

Matrix for this example is below:

To enter the matrix A into the data matrix editor:

• Press [APPS], select the Data/Matrix icon.
• Press [3] [►] [2] [▼] [▼] [A] [▼].
• Press [ALPHA] [3] [3] [ENTER]
• Users with TI-92 family or Voyage 200 may omit pressing [ALPHA] or [2ND] [A-LOCK] during these steps.

• Press [ENTER] [6] [ENTER] [1] [2] [ENTER] [1] [8] [ENTER].
• Press [5] [ENTER] [1] [4] [ENTER] [3] [1] [ENTER].
• Press [3] [ENTER] [8] [ENTER] [1] [8] [ENTER].

• Press [HOME].

To Calculate the LU (lower-upper) decomposition of the matrix:

• Press [2ND] [MATH] [4] [ALPHA] [B].

• Press [ALPHA] [A] [,] [2ND] [A-LOCK].
• Press [L] [O] [W] [E] [R].
• Press [2ND] [A-LOCK] [,] [2ND] [A-LOCK].
• Press [U] [P] [P] [E] [R].
• Press [2ND] [A-LOCK] [,] [2ND] [A-LOCK].
• Press [P] [E] [R] [M] [ENTER].
• Press [2ND] [VAR-LINK] and locate lower.

• Press [ENTER] [ENTER] to display the lower triangular matrix.
• Press [2ND] [VAR-LINK] and locate upper.
• Press [ENTER] [ENTER] to display the upper triangular matrix.
• Press [2ND] [VAR-LINK] and locate perm.
• Press [ENTER] [ENTER]to display the permutation matrix.

Please see the TI-89 family, TI-92 family and Voyage 200 guidebooks for additional information.