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Let T: R2 → R3 be the Linear transformation whose matrixwith 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→ R3 be the Linear transformation whose matrixwith respe...
Let i of 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 map-ping since matrix is 3 x 2 the column of A span R3 if Ahas 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→ R3 be the Linear transformation whose matrixwith respect to standardbasis of R3 and R2 is The 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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