7. Matrix A has three columns. The first and second columns are (1,2,3) and (3,1,-1) respectively. Find the third column if the vector (1,1,1) belongs to the nullspace of the matrix. a) (-4,-3,-2) f) None of the above b) (4,3,2) c) (4,-3,-1) d) (-4,3,2)

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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6. The vector (1,1,-1) belongs to the left nullspace of a matrix. Choose the right
sentence:
a) The matrix has three columns
b) The matrix has three rows and they are linearly independent
c) The third row is equal to the sum of the first and second rows
d) The third column is equal to the sum of the first and second columns of the
matrix
e) None of the above
7. Matrix A has three columns. The first and second columns are (1,2,3) and
(3,1,-1) respectively. Find the third column if the vector (1,1,1) belongs to the
nullspace of the matrix.
a) (-4,-3,-2)
f) None of the above
b) (4,3,2)
c) (4,-3,-1)
d) (-4,3,2)
Transcribed Image Text:6. The vector (1,1,-1) belongs to the left nullspace of a matrix. Choose the right sentence: a) The matrix has three columns b) The matrix has three rows and they are linearly independent c) The third row is equal to the sum of the first and second rows d) The third column is equal to the sum of the first and second columns of the matrix e) None of the above 7. Matrix A has three columns. The first and second columns are (1,2,3) and (3,1,-1) respectively. Find the third column if the vector (1,1,1) belongs to the nullspace of the matrix. a) (-4,-3,-2) f) None of the above b) (4,3,2) c) (4,-3,-1) d) (-4,3,2)
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