Question: Prove Theorem 6.31. [Show that [ui,i+1] < 1, for each i = 1, 2, . . . , n 1, and that |lii| >

Prove Theorem 6.31. [Show that [ui,i+1] < 1, for each i = 1, 2, . . . , n − 1, and that |lii| > 0, for each i = 1, 2, . . . , n. Deduce that det A = det L · det U ≠ 0.]

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