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Exercises 27 and 28 prove special cases of the facts about
Chapter 2, Problem 27E(choose chapter or problem)
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.)Let A be a 3 × 3 matrix.a. Use equation (2) from Section 2.1 to show that rowi. (A) = rowi. (I)·A 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.Example 5:Let Compute E1A, E2A, and E3A, and describe how these products can be obtained by elementary row operations on A.
Questions & Answers
QUESTION:
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.)Let A be a 3 × 3 matrix.a. Use equation (2) from Section 2.1 to show that rowi. (A) = rowi. (I)·A 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.Example 5:Let Compute E1A, E2A, and E3A, and describe how these products can be obtained by elementary row operations on A.
ANSWER:SolutionStep 1Consider a matrix of order 3 × 3 Now, we have to show that row i. (A) = row i. (I)·A where i = 1, 2, 3.