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Exercise 4.4.35

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Starting from $A = (1, - 1, 0, 0)$ , the orthogonal (not orthonormal) vectors $B =$ $(1, 1, - 2, 0)$ and $C = (1, 1, 1, - 3)$ and $D = (1, 1, 1, 1)$ are in the directions of $q_{2}, q_{3}, q_{4}$ . The 4 by 4 and 5 by 5 matrices with integer orthogonal columns (not orthogonal rows, since not orthonormal $Q$ !) are

[\begin{matrix} A & B & C & D \end{matrix}] = [\begin{matrix} 1 & 1 & 1 & 1 \\ - 1 & 1 & 1 & 1 \\ 0 & - 2 & 1 & 1 \\ 0 & 0 & - 3 & 1 \end{matrix}] and [\begin{matrix} 1 & 1 & 1 & 1 & 1 \\ - 1 & 1 & 1 & 1 & 1 \\ 0 & - 2 & 1 & 1 & 1 \\ 0 & 0 & - 3 & 1 & 1 \\ 0 & 0 & 0 & - 4 & 1 \end{matrix}]

mathchakra

2023-09-14 08:32

Exercise 4.4.35

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