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Prove that the nonzero row vectors of a matrix in row-echelon form are linearly independent. Let = A be an m xn matrix in row-echelon form. If the first column of A is not all zero and e,., em e, denote leading ones, then the nonzero row vectors r,, r, of A, have the form of r. --Select-- --Select-- Select- ra = and so forth. Then, the equation c,r, + c,r, + . + cr = 0 implies which of the following equations? (Select all that apply.) O cgean = 0 Oceim + Cze2m = 0 O c,ean + Cze3n + Cze3n = 0 O c,e2m + cze2m = 0 O c,e1 = 0 O ce, + cze2n + czean = 0 You can conclude in turn that c, = C2 and so the row vectors are linearly independent.

Prove that the nonzero row vectors of a matrix in row-echelon form are linearly independent. Let = A be an m xn matrix in row-echelon form. If the first column of A is not all zero and e,., em e, denote leading ones, then the nonzero row vectors r,, r, of A, have the form of r. --Select-- --Select-- Select- ra = and so forth. Then, the equation c,r, + c,r, + . + cr = 0 implies which of the following equations? (Select all that apply.) O cgean = 0 Oceim + Cze2m = 0 O c,ean + Cze3n + Cze3n = 0 O c,e2m + cze2m = 0 O c,e1 = 0 O ce, + cze2n + czean = 0 You can conclude in turn that c, = C2 and so the row vectors are linearly independent.

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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Prove that the nonzero row vectors of a matrix in row-echelon form are linearly independent. Let = A be an m xn matrix in row-echelon form. If the first column of A is not all zero and e,., e. e, denote leading ones, then the nonzero row vectors r,, r, of A, have the form of Select--- Select--- ---Select-- -Select-- (0. .... 0, 0,. 0, e:,:) (0, (0, .... 0, 0, . 0, esa, ) and so forth. 0, ezm, *, esa, ) Then, the equatio (ess. .... ezm, , e32, **) = 0 implies which of the following equations? (Select all that apply.) (ess,*, esm, **, eis, ) O Cze3n = 0 (0.... 0. ezm, **. e ) Ce1m + C2º2m = 0 Ce3n + C2@3n + C3e3n Ce2m + C2º2m ce11 = 0 Uc̟en + c,e2n + Cze3, = 0 and so the row vectors are linearly independent. = … = C, You can conclude in turn that c, = c, 口0
Transcribed Image Text:Prove that the nonzero row vectors of a matrix in row-echelon form are linearly independent. Let = A be an m xn matrix in row-echelon form. If the first column of A is not all zero and e,., e. e, denote leading ones, then the nonzero row vectors r,, r, of A, have the form of Select--- Select--- ---Select-- -Select-- (0. .... 0, 0,. 0, e:,:) (0, (0, .... 0, 0, . 0, esa, ) and so forth. 0, ezm, *, esa, ) Then, the equatio (ess. .... ezm, , e32, **) = 0 implies which of the following equations? (Select all that apply.) (ess,*, esm, **, eis, ) O Cze3n = 0 (0.... 0. ezm, **. e ) Ce1m + C2º2m = 0 Ce3n + C2@3n + C3e3n Ce2m + C2º2m ce11 = 0 Uc̟en + c,e2n + Cze3, = 0 and so the row vectors are linearly independent. = … = C, You can conclude in turn that c, = c, 口0
Prove that the nonzero row vectors of a matrix in row-echelon form are linearly independent. Let = A be an m x n matrix in row-echelon form. If the first column of A is not all zero and e,., e., enn denote leading ones, then the nonzero row vectors r,r, of A, have the form of -Select-- --Select- Select--- and so forth. Then, the equation c,r, + + cr, = 0 implies which of the following equations? (Select all that apply.) = 0 Ce1m + C,e,2m = 0 U Ce3n + C2ºan + Czº3n = 0 Uce,m + Cze2m = 0 O c,e, = 0 Oce,, + C,e2n + C3®3n = 0 You can conclude in turn that c, = C, = * = O and so the row vectors are linearly independent.
Transcribed Image Text:Prove that the nonzero row vectors of a matrix in row-echelon form are linearly independent. Let = A be an m x n matrix in row-echelon form. If the first column of A is not all zero and e,., e., enn denote leading ones, then the nonzero row vectors r,r, of A, have the form of -Select-- --Select- Select--- and so forth. Then, the equation c,r, + + cr, = 0 implies which of the following equations? (Select all that apply.) = 0 Ce1m + C,e,2m = 0 U Ce3n + C2ºan + Czº3n = 0 Uce,m + Cze2m = 0 O c,e, = 0 Oce,, + C,e2n + C3®3n = 0 You can conclude in turn that c, = C, = * = O and so the row vectors are linearly independent.
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