Solved: Find bases for the null spaces of the matrices

Chapter 4, Problem 10E

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QUESTION:

Find bases for the null spaces of the matrices given in. Refer to the remarks that follow Example in Section 4.2. ExampleIn crystallography, the description of a crystal lattice is aided bychoosing a basis {u, v, w} for ?3 that corresponds to three adjacent edges of one “unit cell” of the crystal. An entire lattice is constructed by stacking together many copies of one cell. There are fourteen basic types of unit cells; three are displayed in Figure Figure Example of unit cells.The coordinates of atoms within the crystal are given relative to the basis for the lattice. For instance, identifies the top face-centered atom in the cell in Figure 32.

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QUESTION:

Find bases for the null spaces of the matrices given in. Refer to the remarks that follow Example in Section 4.2. ExampleIn crystallography, the description of a crystal lattice is aided bychoosing a basis {u, v, w} for ?3 that corresponds to three adjacent edges of one “unit cell” of the crystal. An entire lattice is constructed by stacking together many copies of one cell. There are fourteen basic types of unit cells; three are displayed in Figure Figure Example of unit cells.The coordinates of atoms within the crystal are given relative to the basis for the lattice. For instance, identifies the top face-centered atom in the cell in Figure 32.

ANSWER:

Solution 10EStep 1 of 3

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