Determine whether the function involving the n × n matrix A is a linear transformation.T: Mn,n → Mn,n, T(A) = A−1

Question

Determine whether the function involving the n × n matrix A is a linear transformation.T: Mn,n → Mn,n, T(A) = A−1
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Solution 1

To determine whether a function is a linear transformation, it must satisfy two properties:

  1. Additivity: T(A + B) = T(A) + T(B)
  2. Scalar multiplication: T(cA) = cT(A)

where A and B are matrices, and c is a scalar.

Let's check these properties for the function T(A) = A−1.

  1. Additivity:

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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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