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Suppose A is a real n × n matrix of rank r. Let V be the vector space of all real n × n matrices X such that AX = 0. What is the dimension of V?
  • a)
    r
  • b)
    nr
  • c)
    n2r
  • d)
    n2 - nr
Correct answer is option 'D'. Can you explain this answer?
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Suppose A is a real n ×n matrix of rank r. Let V be the vector s...
X n matrix and B is a real n x m matrix. Then, the product AB is a real n x m matrix obtained by multiplying each row of A by each column of B and summing the results. The resulting matrix AB will have n rows and m columns.
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Suppose A is a real n ×n matrix of rank r. Let V be the vector s...
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Suppose A is a real n ×n matrix of rank r. Let V be the vector space of all real n×n matrices X such that AX =0. What is the dimension of V?a)rb)nrc)n2rd)n2- nrCorrect answer is option 'D'. Can you explain this answer?
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