GO Classes | DA Course| Linear Algebra

Answer 1

No, TA is not onto.
Since the column space of A does not span R3

Answer 2

$\mathrm{T}_{\mathbf{A}}$ is onto because the domain is $\mathbb{R}^{2}$ and the co-domain is $\mathbb{R}^{3}$. Intuitively, two vectors are not enough to span $\mathbb{R}^{3}$. Geometrically, two vectors in $\mathbb{R}^{3}$ span a 2D plane going through the origin. The vectors not on the plane $\operatorname{span}\left\{\mathbf{v}_{1}, \mathbf{v}_{2}\right\}$ are not in the range of $\mathrm{T}_{\mathbf{A}}$.

Comments

And that makes it not onto right? 

The rank of transformation matrix A can only be <= 2 and never 3. Hence its not onto transformation.

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How can TA be onto when in A you only have 2 columns in R3, it won't be enough to fill the space of R3 completly to be called as onto.

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Sir justy copied the answer from the slide , obviously Its Not Onto