Question: Determine whether the linear operator T: R2 R2 defined by the equations is one-to-one; if so, find the standard matrix for the inverse operator,

Determine whether the linear operator T: R2 → R2 defined by the equations is one-to-one; if so, find the standard matrix for the inverse operator, and find T-1 (w1, w2).
(a) w1 = x1 + 2x2
w2 = - x1 + x2
(b) w1 = 4x1 - 6x2
w2 = - 2x1 + 3x2

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