DLA Reflect on your understanding

Reflections 10.7 Reflect on your understanding

In addition to the reflection activities below, re-read Section 10.2 Terminology and notation. Be sure you understand each of the new definitions introduced in this chapter, and spend some time committing them to memory.

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1. The role of the adjoint matrix.

Consider the formula

A (adj A) = (det A) I .

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(a)

Briefly explain why the formula is true for all square matrices. (Do not assume the size of the matrix — your explanation should be equally valid for all sizes of square matrices.)

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(b)

Briefly explain the relationship between this formula and the concept of matrix inverse.

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2. Determinants of row equivalent matrices.

Explain why the determinants of two row equivalent matrices must be either both zero or both nonzero.

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3. Cramer’s rule.

Briefly summarize Cramer’s rule and how it follows from the adjoint inversion formula.

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