Concept explainers
Exercises 27 and 28 prove special cases of the facts about elementary matrices stated in the box following Example 5. Here A is a 3 × 3 matrix and I = I3. (A general proof would require slightly more notation.)
27. a. Use equation (1) from Section 2.1 to show that rowi(A) = rowi(I)·A, for i = 1,2,3.
b. Show that if rows 1 and 2 of A are interchanged, then the result may be written as EA, where E is an elementary matrix formed by interchanging rows 1 and 2 of I.
c. Show that if row 3 of A is multiplied by 5, then the result may be written as EA, where E is formed by multiplying row 3 of I by 5.
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Linear Algebra and Its Applications (5th Edition)
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