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Given a homogeneous system Ax = 0 with three equations and six variables. Suppose a basis for the nullspace of A is given by 1 -1 1 1 (i) Find the reduced row echelon form of A. 1 (ii) Suppose is a solution of Aæ = b for some b E R³. Write down a general solution of Ax = b. True or false: The non-homogeneous system Ax = c is consis- (iii) tent for every c E R³. Justify your answer.

Given a homogeneous system Ax = 0 with three equations and six variables. Suppose a basis for the nullspace of A is given by 1 -1 1 1 (i) Find the reduced row echelon form of A. 1 (ii) Suppose is a solution of Aæ = b for some b E R³. Write down a general solution of Ax = b. True or false: The non-homogeneous system Ax = c is consis- (iii) tent for every c E R³. Justify your answer.

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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Given a homogeneous system Ax = 0 with three equations and six variables. Suppose a basis for the nullspace of A is given by 1 1 1 -1 1 1 (i) Find the reduced row echelon form of A. 1 (ii) Suppose 1 is a solution of Ax = b for some b e R³. Write 1 1 1 down a general solution of Ax = b. True or false: The non-homogeneous system Ax = c is consis- (iii) tent for every c € R³. Justify your answer. %3D If B is a 3 x 3 invertible matrix, find a basis for the nullspace of (iv) BA. Explain how you derive the answer.
Transcribed Image Text:Given a homogeneous system Ax = 0 with three equations and six variables. Suppose a basis for the nullspace of A is given by 1 1 1 -1 1 1 (i) Find the reduced row echelon form of A. 1 (ii) Suppose 1 is a solution of Ax = b for some b e R³. Write 1 1 1 down a general solution of Ax = b. True or false: The non-homogeneous system Ax = c is consis- (iii) tent for every c € R³. Justify your answer. %3D If B is a 3 x 3 invertible matrix, find a basis for the nullspace of (iv) BA. Explain how you derive the answer.
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