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1) Let A = 1 1 0 2 0 03 2-1-1 0 1 4 1 00 0 0 4 0 10 1 0 1 Solve the followings considering the system AX = Y. a) Find invertible Q such that QA = R where R is the row-reduced echelon form. b) Find a basis for the row space W of A. c) Describe the vectors in W. d) Find coordinates of any 3 EW in ordered basis found in b). e) Write each EW as a linear combination of rows of A. f) Describe V= (X: AX=0}. g) Find a basis for V.

1) Let A = 1 1 0 2 0 03 2-1-1 0 1 4 1 00 0 0 4 0 10 1 0 1 Solve the followings considering the system AX = Y. a) Find invertible Q such that QA = R where R is the row-reduced echelon form. b) Find a basis for the row space W of A. c) Describe the vectors in W. d) Find coordinates of any 3 EW in ordered basis found in b). e) Write each EW as a linear combination of rows of A. f) Describe V= (X: AX=0}. g) Find a basis for V.

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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1) Let A = 1 1 0 2 0 03 2-1-1 0 1 4 1 00 0 0 4 0 10 1 0 1 Solve the followings considering the system AX = Y. a) Find invertible Q such that QA = R where R is the row-reduced echelon form. b) Find a basis for the row space W of A. c) Describe the vectors in W. d) Find coordinates of any 3 EW in ordered basis found in b). e) Write each EW as a linear combination of rows of A. f) Describe V= (X: AX=0}. g) Find a basis for V.
Transcribed Image Text:1) Let A = 1 1 0 2 0 03 2-1-1 0 1 4 1 00 0 0 4 0 10 1 0 1 Solve the followings considering the system AX = Y. a) Find invertible Q such that QA = R where R is the row-reduced echelon form. b) Find a basis for the row space W of A. c) Describe the vectors in W. d) Find coordinates of any 3 EW in ordered basis found in b). e) Write each EW as a linear combination of rows of A. f) Describe V= (X: AX=0}. g) Find a basis for V.
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