SOLUTION: Show that the inner product ⟨u, v⟩ = 5u1v1 − u1v2 − u2v1 + 10u2v2 is the inner product on R2 generated by the matrix A=
| 2 1 |
| -1 3 |
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Question 1167650: Show that the inner product ⟨u, v⟩ = 5u1v1 − u1v2 − u2v1 + 10u2v2 is the inner product on R2 generated by the matrix A=
| 2 1 |
| -1 3 |
Answer by Resolver123(6) (Show Source): You can put this solution on YOUR website!
We have to show that the inner product defined by ⟨𝑢,𝑣⟩ = produces the expression:
⟨𝑢,𝑣⟩ = .
Let and .
These imply that and .
These give
The proof is complete.
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