Consider the linear map A : R3 ----> R3 given by
A(x1, x2, x3) = (x1 − x2,−x1 + x2, x3).
(a) Find the adjoint map [itex]A^*[/itex].
(b) Obtain the matrix representations of A and A* with respect to the canonical basis [itex]f_1[/itex] = [1, 2, 1], [itex]f_2[/itex] = [1, 3, 2], [itex]f_3[/itex] = [0, 1, 2].
The Attempt at a Solution
I am not worried about finding the adjoint right now.
I first want to find the matrix representation of the linear map A.
so we have A(x1, x2, x3) = (x1 − x2,−x1 + x2, x3).
[1 -1 0]
[-1 1 0] = A
[ 0 0 1]
Is that correct?
If that is correct, I then find the adjoint by using the formula, and I get,
[1 1 0]
[1 1 0] = A*
[0 0 1]
Can somebody confirm these please?
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