In Exercises 1–4 , determine whether the operators T 1 and T 2 commute; that is, whether T 1 ∘ T 2 = T 2 ∘ T 1 . T 1 : R 3 → R 3 is the reflection about the xy -plane and T 2 : R 3 → R 3 is the orthogonal projection onto the yz -plane.
In Exercises 1–4 , determine whether the operators T 1 and T 2 commute; that is, whether T 1 ∘ T 2 = T 2 ∘ T 1 . T 1 : R 3 → R 3 is the reflection about the xy -plane and T 2 : R 3 → R 3 is the orthogonal projection onto the yz -plane.
Find bilinear transformation which
transforms the points z = 1, 0, ∞ into the points w = -1, 1, i
respectively.
Let
Let T: R² R² be the linear transformation satisfying
Find the image of an arbitrary vector
·C
*(CE)-[
v₁ =
- [21]
T(v₁) =
and v₂ =
Q
-[4].
and T(√₂) =
·O·
7. Compute the orthogonal projection of
origin.
onto the line through
2
and the
Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)
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