Questionnnnnnn a. Let V and W be vector spaces and T : V → W a...

Questionnnnnnn

a. Let V and W be vector spaces and T : V → W a linear transformation. If {T(v1), . . . T(vn)} is linearly independent in W, show that {v1, . . . vn} is linearly independent in V .

b. Define similar matrices

c Let A1, A2 and A3 be n × n matrices. Show that if A1 is similar to A2 and A2 is similar to A3, then A1 is similar to A3.

d. Show that similar matrices have the same characteristic polynomial and eigenvalues.

e. Determine whether the following mappings are linear transformations.

T : V → R defined by T(x) = hx, vi, where v is a fixed nonzero vector in the real inner product space V .

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Expert Solution

milcah answered 1 year ago

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