Let S be a plane in R3 passing through the origin, so that S is a...

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Let S be a plane in R3 passing through the origin, so that S is a two-dimensional subspace of R³. Say that a linear transformations T: R³ R³ is a reflection about S if T(v) = v for any vector v in S and T(n) = -n whenever n is perpendicular to S. Let T be the linear transformation given by T(x) = Ax, where A is the matrix -2 2 -2 2 1 2 1 2 This linear transformation is the reflection about a plane S. Find a basis for S. A Let S be a plane in R3 passing through the origin, so that S is a two-dimensional subspace of R³. Say that a linear transformations T: R³ R³ is a reflection about S if T(v) = v for any vector v in S and T(n) = -n whenever n is perpendicular to S. Let T be the linear transformation given by T(x) = Ax, where A is the matrix -2 2 -2 2 1 2 1 2 This linear transformation is the reflection about a plane S. Find a basis for S. A