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Introduction to Linear Algebra

Exercise 2.6.18

Answers

(a): Multiply $LDU = L_{1} D_{1} U_{1}$ by inverses to get $L_{1}^{- 1} LD = D_{1} U_{1} U^{- 1}$ . The left side is lower triangular, the right side is upper triangular $\Rightarrow$ both sides are diagonal.
(b): $L, U, L_{1}, U_{1}$ have diagonal 1’s so $D = D_{1}$ . Then $L_{1}^{- 1} L$ and $U_{1} U^{- 1}$ are both $I$ .

mathchakra

2021-12-20 21:12

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