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Matrix B was obtained by row reducing A. 2 -8 4 -8 -1 11 – 46 17 – 46 – 15 A = %3D 1 10 – 42 15 – 42 – 14 - - - - 2 7 - 24 24 - 24 1 1 0 2 5 2 4 0 1 B = –4 2 -4 -1 0 0 0 0 What is the dimension of the row space of B? What is the dimension of the row space of A? What is the dimension of the column space of B? What is the dimension of the column space of A? What is the rank of A? Think about what basis vectors you could use for each of the row/column spaces of A andB - it is possible to find them simply from the given information.

Matrix B was obtained by row reducing A. 2 -8 4 -8 -1 11 – 46 17 – 46 – 15 A = %3D 1 10 – 42 15 – 42 – 14 - - - - 2 7 - 24 24 - 24 1 1 0 2 5 2 4 0 1 B = –4 2 -4 -1 0 0 0 0 What is the dimension of the row space of B? What is the dimension of the row space of A? What is the dimension of the column space of B? What is the dimension of the column space of A? What is the rank of A? Think about what basis vectors you could use for each of the row/column spaces of A andB - it is possible to find them simply from the given information.

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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Matrix B was obtained by row reducing A. - 8 4 - 8 2 1 11 – 46 17 - 46 15 - - A = -1 10 – 42 15 - 42 – 14 2 7 – 24 24 – 24 1 - 1 0 2 2 4 0 1 B = 0 0 - 4 2 - 4 - 1 0 0 What is the dimension of the row space of B? What is the dimension of the row space of A? What is the dimension of the column space of B? What is the dimension of the column space of A? What is the rank of A? Think about what basis vectors you could use for each of the row/column spaces of A and B - it is possible to find them simply from the given information.
Transcribed Image Text:Matrix B was obtained by row reducing A. - 8 4 - 8 2 1 11 – 46 17 - 46 15 - - A = -1 10 – 42 15 - 42 – 14 2 7 – 24 24 – 24 1 - 1 0 2 2 4 0 1 B = 0 0 - 4 2 - 4 - 1 0 0 What is the dimension of the row space of B? What is the dimension of the row space of A? What is the dimension of the column space of B? What is the dimension of the column space of A? What is the rank of A? Think about what basis vectors you could use for each of the row/column spaces of A and B - it is possible to find them simply from the given information.
Matrix B was obtained by row reducing matrix A. 2 4 - 10 – 4 - 2 – 10 11 20 - 45 – 12 - - - A = 2 10 - 9 – 16 35 - 1 - 7 – 13 30 9. 8 40 - 37 – 66 145 34 1 5 0 1 -5 -5 0 0 1 2 - 5 - 2 0 0 0 0 %3D 0 0 0 0 0 0 0 0 What is the nullity of A (i.e. the dimension of the null space)?
Transcribed Image Text:Matrix B was obtained by row reducing matrix A. 2 4 - 10 – 4 - 2 – 10 11 20 - 45 – 12 - - - A = 2 10 - 9 – 16 35 - 1 - 7 – 13 30 9. 8 40 - 37 – 66 145 34 1 5 0 1 -5 -5 0 0 1 2 - 5 - 2 0 0 0 0 %3D 0 0 0 0 0 0 0 0 What is the nullity of A (i.e. the dimension of the null space)?
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