(a) Let T: R^2 ---> R^3 be a linear transformation such that T(i)= (-1, 2, 3) and T(j)= (2, 5, 6). Let v= (a, b); calculate T(v). (b) Let M be the 3x2 matrix whose two columns are given by T(i) and T(j) respectively. If the vectors are represented by column vectors, for example v= | a | | b | show that then T(v) = M(v). We say that matrix M represents the linear transformation T. (c) Which matrix represents the linear transformation T: R^2 --> R^2 of rotating 90 degrees counter-clockwise? Illustrate the transformation to help you.
We say that T: R^n --> R^m is a linear transformation if we have that T associates with any vector of v E R^n a vector T(v) E^m and that , for any scalar a E R and for all
(a) Let T: R^2 ---> R^3 be a linear transformation such that T(i)= (-1, 2, 3) and T(j)= (2, 5, 6). Let v= (a, b); calculate T(v).
(b) Let M be the 3x2 matrix whose two columns are given by T(i) and T(j) respectively. If the vectors are represented by column vectors, for example v= | a |
| b | show that then T(v) = M(v). We say that matrix M represents the linear transformation T.
(c) Which matrix represents the linear transformation T: R^2 --> R^2 of rotating 90 degrees counter-clockwise? Illustrate the transformation to help you.
(d) Use the results of (b) and (c) to find the coordinates of the vector T(v) where v=(-3, 7).
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