1. Suppose A is a matrix with m rows and n columns, and rank A = r. In each part below there is a statement about the equation A = And four conditions relating m,n, and r. Circle the correct condition for each part and give an example of a possible reduce row echelon form matrix R = r*ref(A) for such a matrix A a) There gre infinitely many solutions to A$ =B for every op tion A: ren and rcm option C:r=m and mcn Option B: r=n and ncm Option D: r=h and m=n b) A = 5 has exactly one solution & for every option A: rcn and ram option C: r=m and mcn option B:r=n and nam op tion D: r=n and m=n c) AZ = 6 has no solution for some Bi and the s0lution ī to AX =B has free variables for other t %3D option A : ren and rem option C:r= m and mcn option B:r=n and nam option D: r=n and m=n d) AR =B has no solution for some Ď, and the equation AR =P has exactly one solution R for other ē %3D option A: ran and ram op tion C:r:m and mcn option B:r=n and nam op tion D:r=n and m=n

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Answer the following question accordingly:
1. Suppose A is a matrix with m rows and n columns, and rank A =r. In
each part below there is a statement about the equation A = 6 And four
conditions relating m,n, and r. Circle the correct condition for each part
and give an example of a possible reduce row echelon form matrix R
r*ref(A) for such a matrix A
%3D
a) There gre infinitely many solutions to A$ =B for
every B
%3D
op tion A: ren and rem
option C:r=m and mcn
option B: r=n and ncm
Option D: r=h and m=n
b) AR = 5 has exactly one solution R for every
option A: rcn and ram
option C: r=m and mcn
option B:r=n and nam
op tion D: ran and m=n
c) AR = 5 has no solution for some B, and the solution ĕ
to A& =B has free variables for other B
option A: ren and rem
option C:r=m and mcn
option B:r=n and nem
option D:r=n and m=n
d) A& =B has no solution for some B, and the equation
AP =B has exactly one solution P for other
option B:r=n and
op fion D:r:n and m=n
option A :
:rsn and
n<m
op tion C:r:m and mcn
Transcribed Image Text:1. Suppose A is a matrix with m rows and n columns, and rank A =r. In each part below there is a statement about the equation A = 6 And four conditions relating m,n, and r. Circle the correct condition for each part and give an example of a possible reduce row echelon form matrix R r*ref(A) for such a matrix A %3D a) There gre infinitely many solutions to A$ =B for every B %3D op tion A: ren and rem option C:r=m and mcn option B: r=n and ncm Option D: r=h and m=n b) AR = 5 has exactly one solution R for every option A: rcn and ram option C: r=m and mcn option B:r=n and nam op tion D: ran and m=n c) AR = 5 has no solution for some B, and the solution ĕ to A& =B has free variables for other B option A: ren and rem option C:r=m and mcn option B:r=n and nem option D:r=n and m=n d) A& =B has no solution for some B, and the equation AP =B has exactly one solution P for other option B:r=n and op fion D:r:n and m=n option A : :rsn and n<m op tion C:r:m and mcn
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