Science:Math Exam Resources/Courses/MATH221/December 2009/Question 12 (c)

MATH221 December 2009

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Question 12 (c)
Mark each statement either True or False. You do not have to justify your answer. If the matrix A has 6 rows and 9 columns, then dim(N(A)) ≥ 3.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint

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Solution
Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. True. By the rank nullity theorem $dim(N(A))=n-rank(A)$ $n=9$ (columns) The rank is the number of linearly independent columns of A, in this case is at the most 6, likewise dim(N(A)) ≥ 3.