Question

a. Let →u = (x, y, z) ∈ R^3 and define T : R^3 → R^3...

a. Let →u = (x, y, z) ∈ R^3 and define T : R^3 → R^3 as

T( →u ) = T(x, y, z) = (x + y, 2z − y, x − z)

Find the standard matrix for T and decide whether the map T is invertible.

If yes then find the inverse transformation, if no, then explain why.

b. Let (x, y, z) ∈ R^3 be given T : R^3 → R^2 by T(x, y, z) = (x + 2y, x + y + z)

Find the standard matrix to T and decide whether the map T is invertible.

If yes then find the inverse transformation, if no, then explain why.

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