 Solution

ID: past-exam-of-the-algebra-analysis-and-differential-equations-1-course-of-the-university-of-oxford/2011/1/b/ii/solution

The span

U

is the coordinate plane

{(x_{1}, x_{2}, 0, 0)^{T}}

U^{\circ} = span {ε_{3}, ε_{4}}

. The dual map is composition with

T

, so

T^{'} ε_{3} = ε_{3}, T^{'} ε_{4} = 0.

T^{'} (U^{\circ}) = span {ε_{3}} .

Equivalently,

T^{'} (a ε_{3} + b ε_{4})

sends

x

a x_{3}

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