Problem 2. [10 pts] Recall that the space of 2 2 matrices R22 is a vector...

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Problem 2. [10 pts] Recall that the space of 2 2 matrices R22 is a vector space with the usual addition and scalar multiplication. Determine (with justification) whether the following subsets of R22 are subspaces or not: 1. (5pts) S = {(o b) Rx a, b R } diagonal, and bottom left corner always 0) Is it a subspace? Yes No (The set of matrices with equal entries in the 2. (5pts) Fix some 2 x 2 matrix A = SA = {M R22|MA = AM}. Is it a subspace? Yes No (a) 1 3 For instance A = And consider: 2 3 (The set of matrices that commute with A) Problem 2. [10 pts] Recall that the space of 2 2 matrices R22 is a vector space with the usual addition and scalar multiplication. Determine (with justification) whether the following subsets of R22 are subspaces or not: 1. (5pts) S = {(o b) Rx a, b R } diagonal, and bottom left corner always 0) Is it a subspace? Yes No (The set of matrices with equal entries in the 2. (5pts) Fix some 2 x 2 matrix A = SA = {M R22|MA = AM}. Is it a subspace? Yes No (a) 1 3 For instance A = And consider: 2 3 (The set of matrices that commute with A)