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PROBLEM 2: It can be shown that the set M of all matrices of the form numbers, is a subspace of M22, the space of all 2 2 matrices with real entries. It can be also shown that the standard basis for M is a subset of the standard basis is E- referred for simplicity as&(e2, e3 }. with b, c real Find the vector of coordinate of A- a) b) Show that the set of matrices B-(bi, b2j- 5 ol in the basis 0 11 r0 C ? il} is linear independent Hint: You can use the vector of coordinates of bi, b2 in the basis E, or go with the definition of linear independence in a general vector space. c) Justify why B is a basis for M d) Find PBE, the change of basis matrix from basis B to basis & and PEB, the change of basis matrix from basis to basis B. Verify that PEB is the inverse of PBE. Comment if this would be true for any other basis of M e) PROBLEM 2: It can be shown that the set M of all matrices of the form numbers, is a subspace of M22, the space of all 2 2 matrices with real entries. It can be also shown that the standard basis for M is a subset of the standard basis is E- referred for simplicity as&(e2, e3 }. with b, c real Find the vector of coordinate of A- a) b) Show that the set of matrices B-(bi, b2j- 5 ol in the basis 0 11 r0 C ? il} is linear independent Hint: You can use the vector of coordinates of bi, b2 in the basis E, or go with the definition of linear independence in a general vector space. c) Justify why B is a basis for M d) Find PBE, the change of basis matrix from basis B to basis & and PEB, the change of basis matrix from basis to basis B. Verify that PEB is the inverse of PBE. Comment if this would be true for any other basis of M e)