Consider the following bases B and B' for some subspace of M2x2(R), the vector space of all 2 by 2 matrices over R. -{[: :] [}]- [ :]} «-{{; :]- [; :] [: :} {[: ]. 1 0 3 0 0 1 1 1 3 1 3 0 0 В B' 2 3 4...

Consider the following bases B and B' for some subspace of M2x2(R), the vector space<br>of all 2 by 2 matrices over R.<br>-{[: :] [}]- [ :]} «-{{; :]- [; :] [: :}<br>{[: ].<br>1 0<br>3 0<br>0 1<br>1<br>1<br>3 1<br>3<br>0 0<br>В<br>B'<br>2 3<br>4 3<br>2 1<br>0 -8<br>3 4<br>-6 -1<br>(a) Find the coordinate matrix of A =<br>4<br>relative to the basis B', that is<br>6.<br>[x(A)]g

Extracted text: Consider the following bases B and B' for some subspace of M2x2(R), the vector space of all 2 by 2 matrices over R. -{[: :] [}]- [ :]} «-{{; :]- [; :] [: :} {[: ]. 1 0 3 0 0 1 1 1 3 1 3 0 0 В B' 2 3 4 3 2 1 0 -8 3 4 -6 -1 (a) Find the coordinate matrix of A = 4 relative to the basis B', that is 6. [x(A)]g". (b) Calculate the transition matrix PB→B. [Show steps.] (c) Use part 2(b) to calculate the coordinate matrix of A relative to the basis B. (d) Verify the coordinate matrix obtained in part 2(c).

Jun 05, 2022

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Consider the following bases B and B' for some subspace of M2x2(R), the vector space of all 2 by 2 matrices over R. -{[: :] [}]- [ :]} «-{{; :]- [; :] [: :} {[: ]. 1 0 3 0 0 1 1 1 3 1 3 0 0 В B' 2 3 4...

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