Problem 6. Consider row operations on matrices with 4 rows. Recall that for each row operation there is a corresponding 4 × 4 elementary matrix E so that EA is the same as the matrix obtained by applying the row operation to A. (Consider each part of the problem separately, don't chain the operations together.) When the problem asks for the inverse row operation give it in the form we've been using, e.g., R3 + R3+2R1. A. Consider the row operation R1 → R3. i.) Find the corresponding elementary matrix E. ii.) Find the inverse row operation. iii.) Find the inverse of E B. Consider the row operation R4 + 5R4. i.) Find the corresponding elementary matrix E. ii.) Find the inverse row operation. iii.) Find the inverse of E C. Consider the row operation R1 + R1 +2R4 i.) Find the corresponding elementary matrix E. ii.) Find the inverse row operation. iii.) Find the inverse of E.

Problem 6. Consider row operations on matrices with 4 rows. Recall that for each row operation there is a corresponding 4 × 4 elementary matrix E so that EA is the same as the matrix obtained by applying the row operation to A. (Consider each part of the problem separately, don't chain the operations together.) When the problem asks for the inverse row operation give it in the form we've been using, e.g., R3 + R3+2R1. A. Consider the row operation R1 → R3. i.) Find the corresponding elementary matrix E. ii.) Find the inverse row operation. iii.) Find the inverse of E B. Consider the row operation R4 + 5R4. i.) Find the corresponding elementary matrix E. ii.) Find the inverse row operation. iii.) Find the inverse of E C. Consider the row operation R1 + R1 +2R4 i.) Find the corresponding elementary matrix E. ii.) Find the inverse row operation. iii.) Find the inverse of E.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Problem 6. Consider row operations on matrices with 4 rows.
Recall that for each row operation there is a corresponding 4 x 4 elementary
matrix E so that EA is the same as the matrix obtained by applying the row
operation to A.
(Consider each part of the problem separately, don't chain the operations
together.)
When the problem asks for the inverse row operation give it in the form
we've been using, e.g., R3 + R3+2R1.
A. Consider the row operation R1 → R3.
i.) Find the corresponding elementary matrix E.
ii.) Find the inverse row operation.
iii.) Find the inverse of E
B. Consider the row operation R4 + 5R4.
i.) Find the corresponding elementary matrix E.
ii.) Find the inverse row operation.
iii.) Find the inverse of E
C. Consider the row operation R1 + R1 + 2R4
i.) Find the corresponding elementary matrix E.
ii.) Find the inverse row operation.
iii.) Find the inverse of E.

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This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise In the matrix shown below, form a row-equivalent matrix by multiplying row 1 by -6 and adding the result to row 2. In other words, apply the row operation (R₂-6R₁) to the given matrix. -8 5 5 1 6 84 5 Step 1 Perform elementary row operations to form a row-equivalent matrix. Add -6 times row 1 to row 2 and put the result in row 2. 1 1 -8 5 6 5 1 8 4 5 R₂-6R₂ -6(1) 5- -8 (-8) 1-6 5 8 -4 5 Simplifying all values gives the following matrix, which is row-equivalent to the original matrix.