# Linear operators proof

(See attached file for full problem description)

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Let V be a two-dimensional vector space over the field F, and let be an ordered

basis for V. If is a linear operator and then prove that

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https://brainmass.com/math/discrete-math/linear-operators-proof-67667

#### Solution Preview

........(1)

Here zero operator and identity operator will have the same matrix with respect to any basis namely the zero matrix and identity matrix ,therefore we need to check the equality with respect to basis = M

M^2= * =

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#### Solution Summary

This is a proof regarding linear operators and two-dimensional vector space.

$2.19