Matrix of the change of basis

Task number: 2566

Let \(A=((1{,}2,0{,}1)^T,(4{,}1,3{,}1)^T,(3{,}1,3{,}4)^T,(2{,}0,2{,}2)^T)\),
be two bases of \(\mathbb Z_5^4\). Determine the matrices of the change of basis:

  • Variant 1

    \([id]_{AK}\), i.e. from the basis \(A\) to the canonical basis.

  • Variant 2

    \([id]_{KB}\), i.e. from the canonical basis to the basis \(B\).

  • Variant 3

    \([id]_{AB}\), i.e. from the basis \(A\) to the basis \(B\).

Difficulty level: Easy task (using definitions and simple reasoning)
Solution require uncommon idea
Cs translation
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