Homework SourseIf T R3 rightarrow R2 is a linear transformation such that T
If T: R^3 rightarrow R^2 is a linear transformation such that T[1 0 0] = [-1 -3], T[0 1 0] = [-1 0], and T[0 0 1] = [3 5], that the matrix that represents T is []
![If T: R^3 rightarrow R^2 is a linear transformation such that T[1 0 0] = [-1 -3], T[0 1 0] = [-1 0], and T[0 0 1] = [3 5], that the matrix that represents T is](/WebImages/40/if-t-r3-rightarrow-r2-is-a-linear-transformation-such-that-t-1123546-1761598499-0.webp "If T: R^3 rightarrow R^2 is a linear transformation such that T[1 0 0] = [-1 -3], T[0 1 0] = [-1 0], and T[0 0 1] = [3 5], that the matrix that represents T is")
Solution
We know that the matrix with images of the vectors (1,0,0)T, (0,1,0)T and (0,0,1)T as columns is the standard matrix of T. Hence, the standard matrix of T is A=
-1
-1
3
-3
0
5
| -1 | -1 | 3 |
| -3 | 0 | 5 |
