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Let  A be a m × n matrix with row rank = r = column rank. The dimension of the space of solution of the system of linear equations AX = 0 is :
  • a)
    n – r
  • b)
    n + r 
  • c)
    r
  • d)
    min(m,n) – r
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
LetAbe am × nmatrix with row rank =r= column rank. The dimension...
Given that rank  A = r
⇒ There would be r  linearly independent solutions
Dim (A) = dim  – rank = n – r
The correct answer is: n – r
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LetAbe am × nmatrix with row rank =r= column rank. The dimension...
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LetAbe am × nmatrix with row rank =r= column rank. The dimension of the space of solution of the system of linear equationsAX= 0is :a)n–rb)n+rc)rd)min(m,n) –rCorrect answer is option 'A'. Can you explain this answer?
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