upper triangular form
[upper triangular form|upper triangular form] The goal is to eliminate one variable at a time to achieve upper triangular form, the ideal form for a three-by-three system.
Definition
upper triangular form The goal is to eliminate one variable at a time to achieve upper triangular form, the ideal form for a <a href='/en/entity/three-by-three-system'>three-by-three system</a>. This form allows straightforward back-substitution to find a solution (x, y, z), an ordered triple.
Mechanism
upper triangular form To write the system in upper triangular form, perform operations that eliminate one variable at a time. This process achieves the ideal form for a <a href='/en/entity/three-by-three-system'>three-by-three system</a>, enabling straightforward back-substitution to find an ordered triple (x, y, z).
Examples
upper triangular form If the matrix is in upper triangular form, the determinant equals the product of entries down the main diagonal.