Practice question · Select all that apply
T is a linear map from three-dimensional space into the plane. Select every statement that MUST be true.
Hints
- Four options restate linearity; one is about the SHAPE of the matrix.
- The matrix must multiply a 3-entry column and produce a 2-entry column.
Show the answer
- A. T(2u) = 2 T(u) for every u
- B. T(u + v) = T(u) + T(v) for all u and v
- C. T sends (0, 0, 0) to (0, 0)
- D. T(u - v) = T(u) - T(v) for all u and v
Why
Linearity gives the origin, scaling, additivity and hence subtraction. But the matrix is 2x3, not 3x2: it has one column per input coordinate and one row per output coordinate. Reversing the convention is the standard shape error.
Practise Linear Transformations
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