1 3 0 3 1 4 1 2 -1 -1 -1 1 0. B = 1 %3D 3 -4 4 2 -8 %3D 6. 7 0 3 -1 2 9 5-7 17. How many rows of A contain a pivot position? Does the equation Ax = b have a solution for each b in R4? %3D 18. Can every vector in R4 be written as a linear combination of the columns of the matrix B above? Do the columns of B span R3?

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 69E: Consider an mn matrix A and an np matrix B. Show that the row vectors of AB are in the row space of...
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Number 18 show all work 

1
3 0 3
1
4
1 2
-1
-1 -1 1
0.
B =
1
%3D
3 -4
4
2 -8
%3D
6.
7
0 3 -1
2 9 5-7
17. How many rows of A contain a pivot position? Does the
equation Ax = b have a solution for each b in R4?
%3D
18. Can every vector in R4 be written as a linear combination of
the columns of the matrix B above? Do the columns of B
span R3?
Transcribed Image Text:1 3 0 3 1 4 1 2 -1 -1 -1 1 0. B = 1 %3D 3 -4 4 2 -8 %3D 6. 7 0 3 -1 2 9 5-7 17. How many rows of A contain a pivot position? Does the equation Ax = b have a solution for each b in R4? %3D 18. Can every vector in R4 be written as a linear combination of the columns of the matrix B above? Do the columns of B span R3?
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