Mathematics · Linear Algebra
If T is a linear transformation on V3(F) defined by T(a, b, c) = (a + b, b, a + b + c) for arbitrary (a, b, c) ∈ V3, find T(a1, b1, c1) with respect to the standard inner product basis.
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1T(a1, b1, c1) = (a1 + c1, a1 + b1 + c1, c1)✓
- 2T(a1, b1, c1) = (a1 + c1, b1, c1)
- 3T(a1, b1, c1) = (a1 + c1, c1, a1)
- 4T(a1, b1, c1) = (a1 + c1, b1 + c1, a1 c1)
Correct answer
T(a1, b1, c1) = (a1 + c1, a1 + b1 + c1, c1)
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