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Let T: R2→ R3 be the Linear transformation whose matrix with respect to standard basis of R3 and R2 is  The T
  • a)
     is one to one 
  • b)
     is one to one and onto both 
  • c)
     is onto 
  • d)
     has rank 1
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Let T: R2→ R3be the Linear transformation whose matrix with respe...
Let iof T : R2 → R3 be a Linear transformation such that matrix a with respect to standard basis of T is 
here clearly the columns of A are linearly independent b ⇒ T is one one mapping since matrix is 3 × 2 the column of A span R3 if A has 3 pivot positions but it is contradiction as A has 2 columns only
⇒ Associated Linear transformation is not onto 
Rank of matrix = Rank of Linear transformation = 2 
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Let T: R2→ R3be the Linear transformation whose matrix with respect to standard basis of R3and R2isThe Ta)is one to oneb)is one to one and onto bothc)is ontod)has rank 1Correct answer is option 'A'. Can you explain this answer?
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