Mathematics, 06.05.2020 00:04 lolweapon
Consider the system as Axequals0, where A is a 15times19 matrix. Choose the correct answer below. A. No. Since A has 15 pivot positions, rank Aequals15. By the Rank Theorem, dim Nul Aequals15minusrank Aequals0. Since Nu l Upper A equals 0, it is impossible to find a single vector in Nul A that spans Nul A. B. Yes. Since A has at most 15 pivot positions, rank Aless than or equals15. By the Rank Theorem, dim Nul Aequals19minusrank Agreater than or equals4. Since there is at least one free variable in the system, all solutions are multiples of one fixed nonzero solution. C. Yes. Since A has 15 pivot positions, rank Aequals15. By the Rank Theorem, dim Nul Aequals15minusrank Aequals0. Thus, all solutions are multiples of one fixed nonzero solution. D. No. Since A has at most 15 pivot positions, rank Aless than or equals15. By the Rank Theorem, dim Nul Aequals19minusrank Agreater than or equals4. Thus, it is impossible to find a single vector in Nul A that spans Nul A.
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Consider the system as Axequals0, where A is a 15times19 matrix. Choose the correct answer below. A....
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