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Recall: An mxn matrix has m rows and columns. Tip: Keep it simple. Wherever possible, choose A and b so that the augmented matrix [A | b ] is already in row-echelon form. (Note: This may not always be possible, depending on the requirements given in the question.) (a) Give an example of a 3 x 3 matrix A of rank 2 and a 3 x 1 vector b such that the linear system with augmented matrix [ A ] b] has no solution. A = [ 10 (b) Give an example of a 3 x 2 matrix A with three non-zero rows and a 3 x 1 vector b such that the linear system with augmented matrix [A | b] has the unique solution x = -B3³). b= [][]}] (c) Give an example of a 3 x 4 matrix A and a 3 x 1 vector b such that the solution set of the linear system with augmented matrix [ A | b] is a line in R4 which has direction vector A = b= JU (d) Give an example of a 3 x 5 matrix A such that the linear system [A | b] has at least one solution for every 3 x 1 vector b. A=

Recall: An mxn matrix has m rows and columns. Tip: Keep it simple. Wherever possible, choose A and b so that the augmented matrix [A | b ] is already in row-echelon form. (Note: This may not always be possible, depending on the requirements given in the question.) (a) Give an example of a 3 x 3 matrix A of rank 2 and a 3 x 1 vector b such that the linear system with augmented matrix [ A ] b] has no solution. A = [ 10 (b) Give an example of a 3 x 2 matrix A with three non-zero rows and a 3 x 1 vector b such that the linear system with augmented matrix [A | b] has the unique solution x = -B3³). b= [][]}] (c) Give an example of a 3 x 4 matrix A and a 3 x 1 vector b such that the solution set of the linear system with augmented matrix [ A | b] is a line in R4 which has direction vector A = b= JU (d) Give an example of a 3 x 5 matrix A such that the linear system [A | b] has at least one solution for every 3 x 1 vector b. A=

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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Recall: An mxn matrix has m rows and columns. Tip: Keep it simple. Wherever possible, choose A and b so that the augmented matrix [A | b ] is already in row-echelon form. (Note: This may not always be possible, depending on the requirements given in the question.) (a) Give an example of a 3 x 3 matrix A of rank 2 and a 3 x 1 vector b such that the linear system with augmented matrix [ A ] b] has no solution. A = [ 10 (b) Give an example of a 3 x 2 matrix A with three non-zero rows and a 3 x 1 vector b such that the linear system with augmented matrix [A | b] has the unique solution x = -B3³). b= [][]}] (c) Give an example of a 3 x 4 matrix A and a 3 x 1 vector b such that the solution set of the linear system with augmented matrix [ A | b] is a line in R4 which has direction vector A = b= JU (d) Give an example of a 3 x 5 matrix A such that the linear system [A | b] has at least one solution for every 3 x 1 vector b. A=
Transcribed Image Text:Recall: An mxn matrix has m rows and columns. Tip: Keep it simple. Wherever possible, choose A and b so that the augmented matrix [A | b ] is already in row-echelon form. (Note: This may not always be possible, depending on the requirements given in the question.) (a) Give an example of a 3 x 3 matrix A of rank 2 and a 3 x 1 vector b such that the linear system with augmented matrix [ A ] b] has no solution. A = [ 10 (b) Give an example of a 3 x 2 matrix A with three non-zero rows and a 3 x 1 vector b such that the linear system with augmented matrix [A | b] has the unique solution x = -B3³). b= [][]}] (c) Give an example of a 3 x 4 matrix A and a 3 x 1 vector b such that the solution set of the linear system with augmented matrix [ A | b] is a line in R4 which has direction vector A = b= JU (d) Give an example of a 3 x 5 matrix A such that the linear system [A | b] has at least one solution for every 3 x 1 vector b. A=
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