Consider the basis $S =\{v_1,v_2,v_3\} $ for $R^3$ where $v_1=(1,1,1), v_2=(1,1,0) ,v_3=(1,0,0) $. T is a linear transformation from $R^3$ to $R^2$ such that $T (v_1)=(1,0), T(v_2)= (2,-1) , T(v_3)= (4,3) $. Then $T(2,-3,5)$ is- ?
I am familiar with the concept of linear transformation and I was thinking of first finding the matrix of transformation. But the question gives no information about the basis of $R^2$ but does for $R^3$. However I tried with the basis $(1,0)$ and $(0,1) $ but my answer doesn't match with any of the options.
Best Answer
Since$$(2,-3,5)=5v_1-8v_2+5v_3,$$then $T(2,-3,5)=\cdots$?