Let V be the vector space of all 2*3 real matrices and W be the vector space of all 2 * 2 real matrices. Thena)There is a one-one linear transformation from V to Wb)Kernel of any linear transformation from V to W is non-trivialc)There is an isomorphism from V to Wd)There is an onto linear transformation from W to VCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

If V and W are two vector spaces of finite dimension.

Then T : V →W can be one-one linear transformation only if dim(V) ≤ dim(W) and can be onto linear

transformation only if dim(V) ≥ dim(W)

⇒ option (b) is correct and options (a). (c) and (d) are false.

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