UNDERSTANDING ALGEBRA homework help (Page 4024-4026) - Suppose L V linear V and L(v1 = v1 v2 L(v2 = 2v1 v2 Compute the matrix of L in the basis B and

UNDERSTANDING ALGEBRA homework help (Page 4024-4026) -...

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Suppose L : V linear −−−→ V and L(v1) = v1 + v2 , L(v2) = 2v1 + v2 . Compute the matrix of L in the basis B and then compute the trace of this matrix. Suppose that ad − bc 6= 0 and consider now the new basis B 0 = (av1 + bv2, cv1 + dv2). Compute the matrix of L in the basis B0 . Compute the trace of this matrix. What do you find? What do you conclude about the trace of a matrix? Does it make sense to talk about the “trace of a linear transformation” without reference to any bases? 7. Explain what happens to a matrix when: (a) You multiply it on the left by a diagonal matrix. (b) You multiply it on the right by a diagonal matrix. 148 7.4 Review Problems 149 Give a few simple examples before you start explaining. 8. Compute exp(A) for the following matrices: • A
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