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(d) Show that the system of equations corresponding to the augmented matrix 6 82 1 3 2 -2 -7 0 has no solutions. (e) [challenge] What could happen to the solution set of a linear system when you remove a row from the augmented matrix? What does this tell you about the effect of removing a row on row-equivalence? (f) [challenge] Determine whether the following statements are true or false. If the statement is true, give a 2 to 3 sentence proof. If the statement is false, give a counter example. i. Row-equivalent augmented matrices have the same solution set. ii. Augmented matrices with the same solution set are row-equivalent.

(d) Show that the system of equations corresponding to the augmented matrix 6 82 1 3 2 -2 -7 0 has no solutions. (e) [challenge] What could happen to the solution set of a linear system when you remove a row from the augmented matrix? What does this tell you about the effect of removing a row on row-equivalence? (f) [challenge] Determine whether the following statements are true or false. If the statement is true, give a 2 to 3 sentence proof. If the statement is false, give a counter example. i. Row-equivalent augmented matrices have the same solution set. ii. Augmented matrices with the same solution set are row-equivalent.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I need D , E and F in the order to get positive feedback Please show me neat and clean work Take your time Please solve the given parts please
1. A matriz by any other name¹ Two matrices are row equivalent if one matrix can be changed into another matrix by a series of elementary row operations. (a) Are the following matrices row-equivalent? 3 063 0232 , M₂ = 5-723 M₁ = (b) Removing the 2nd column of each matrix gives 363 032 , M₂ 3 523 M₁ = 3 3 5 6 1 -2 4 2 -13 8 2 3 2 -7 0 12 7 9 5 -7 -3 Use a computational tool to determine whether or not these matrices are row equivalent. 7 3 12 9 5 5-7 -3 (c) Could removing the same column from a pair of equivalent matrices affect row equivalence? If so, give an example. If not, give a short justification. (d) Show that the system of equations corresponding to the augmented matrix has no solutions. (e) [challenge] What could happen to the solution set of a linear system when you remove a row from the augmented matrix? What does this tell you about the effect of removing a row on row-equivalence? (f) [challenge] Determine whether the following statements are true or false. If the statement is true, give a 2 to 3 sentence proof. If the statement is false, give a counter example. i. Row-equivalent augmented matrices have the same solution set. ii. Augmented matrices with the same solution set are row-equivalent.
Transcribed Image Text:1. A matriz by any other name¹ Two matrices are row equivalent if one matrix can be changed into another matrix by a series of elementary row operations. (a) Are the following matrices row-equivalent? 3 063 0232 , M₂ = 5-723 M₁ = (b) Removing the 2nd column of each matrix gives 363 032 , M₂ 3 523 M₁ = 3 3 5 6 1 -2 4 2 -13 8 2 3 2 -7 0 12 7 9 5 -7 -3 Use a computational tool to determine whether or not these matrices are row equivalent. 7 3 12 9 5 5-7 -3 (c) Could removing the same column from a pair of equivalent matrices affect row equivalence? If so, give an example. If not, give a short justification. (d) Show that the system of equations corresponding to the augmented matrix has no solutions. (e) [challenge] What could happen to the solution set of a linear system when you remove a row from the augmented matrix? What does this tell you about the effect of removing a row on row-equivalence? (f) [challenge] Determine whether the following statements are true or false. If the statement is true, give a 2 to 3 sentence proof. If the statement is false, give a counter example. i. Row-equivalent augmented matrices have the same solution set. ii. Augmented matrices with the same solution set are row-equivalent.
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