Prove that t is a linear transformation on r 2 and
Let a, b ∈ R. Consider the function T : R2 → R2 given by
T ( x, y )= (Re[( a + ib )( x + iy )] , Im[( a + ib )( x + iy )]) .
Prove that T is a linear transformation on R2 , and determine a 2 × 2 matrix form for T . What does T represent?
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