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In Example 5 of Section 2.1, the mapping T: M2x2(i) > M2x2(i) defined by T(M) = Ml for

Chapter 2, Problem 19

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QUESTION:

In Example 5 of Section 2.1, the mapping T: M2x2(i?) > M2x2(i?) defined by T(M) = Ml for each M e M2x2(i?) is a linear transformation. Let 0 = {EU ,E12 , E21,E22}, which is a basis for M2x2(R), as noted in Example 3 of Section 1.6. (a) Compute [Tj/3. (b) Verify that LAM M ) = ^T(M ) for A = [T]^ and / M = 1 2 3 4

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QUESTION:

In Example 5 of Section 2.1, the mapping T: M2x2(i?) > M2x2(i?) defined by T(M) = Ml for each M e M2x2(i?) is a linear transformation. Let 0 = {EU ,E12 , E21,E22}, which is a basis for M2x2(R), as noted in Example 3 of Section 1.6. (a) Compute [Tj/3. (b) Verify that LAM M ) = ^T(M ) for A = [T]^ and / M = 1 2 3 4

ANSWER:

Step 1 of 6

The mapping  is defined by

Let

To compute .

First, let us compute .

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