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rad0786
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Homework Statement
I have a linear map T:M(2x2) -------> M(2x2) defined by T(B) = [2 3; 4 0] * B
Find a 4 × 4 matrix representation of this linear transformation with respect to the basis of M(2×2)
Homework Equations
T(B) = [2 3; 4 0] * B
and the basis for M(2X2) is:
[1 0; 0 0]
[0 1; 0 0]
[0 0; 1 0]
[0 0; 0 1]
The Attempt at a Solution
T[1 0; 0 0] = [2 3; 4 0]*[1 0; 0 0] = [2 4; 0 0]
T[0 1; 0 0] = [2 3; 4 0]*[0 1; 0 0] = [0 0; 2 4]
T[0 0; 1 0] = [2 3; 4 0]*[0 0; 1 0] = [3 0; 0 0]
T[0 0; 0 1] = [2 3; 4 0]*[0 0; 0 1] = [0 3; 0 0]
Therefore, the matrix would be:
[2 0 3 0;
4 0 0 3;
0 2 0 0;
0 4 0 0]
Could somebody please veryify this for me.
I'd appreciate that