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**1. 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)

**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]

**3. 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