(e) m = 4, n = 4, and the equation Rx = 0 has no solution. (f) m = 4, n = 4, and the equation Rx = 0 has a nontrivial solution. (g) m = 4, n = 4, and for every c the equations Rx = c have a solution containing a free parameter.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 3AEXP
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Please help me parts e, f, g. Thanks

5. In each part below, give a m x n matrix R in reduced row-echelon form satisfying the given
condition, or explain briefly why it is impossible to do so.
(a) m = 3, n = 4, and the equation Rx
= c has a solution for all c.
(b) m = 3, n = 4, and the equation Rx = 0 has a unique solution.
(c) m = 4, n = 3, and the equation Rx = c has a solution for all c.
(d) m = 4, n = 3, and the equation Rx
= 0 has a unique solution.
%3D
(e) m = 4, n = 4, and the equation Rx = 0 has no solution.
(f) m = 4, n = 4, and the equation Rx
O has a nontrivial solution.
(g) m = 4, n = 4, and for every c the equations Rx
= c have a solution containing a free parameter.
Transcribed Image Text:5. In each part below, give a m x n matrix R in reduced row-echelon form satisfying the given condition, or explain briefly why it is impossible to do so. (a) m = 3, n = 4, and the equation Rx = c has a solution for all c. (b) m = 3, n = 4, and the equation Rx = 0 has a unique solution. (c) m = 4, n = 3, and the equation Rx = c has a solution for all c. (d) m = 4, n = 3, and the equation Rx = 0 has a unique solution. %3D (e) m = 4, n = 4, and the equation Rx = 0 has no solution. (f) m = 4, n = 4, and the equation Rx O has a nontrivial solution. (g) m = 4, n = 4, and for every c the equations Rx = c have a solution containing a free parameter.
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