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Questions › DSE › DSE 2015 › Q36
2 marks, −0.666666666666667Mathematics › Vector spaces, rank and eigenvalues › Linear maps, rank and projectionsHardabout 4 min

DSE 2015 Question 36: Vector spaces, rank and eigenvalues

If PPP is a projector and Q:Rm→RnQ:\mathbb{R}^m\to\mathbb{R}^nQ:Rm→Rn is a linear transformation with R(P)=R(Q)\mathcal{R}(P)=\mathcal{R}(Q)R(P)=R(Q), then

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If P is a projector and Q:ℝ^m→ℝⁿ is a linear transformation with R(P)=R(Q), then (A) QP=P (B) PQ=Q (C) QP=I (D) PQ=I

Also written as: If P is a projector and Q:R^m->R^n is a linear transformation with R(P)=R(Q), then

Vector spaces, rank and eigenvalues has come up 41 times in 6 exams since 2008.

What this question tests

This question is on Linear maps, rank and projections, part of Vector spaces, rank and eigenvalues in Mathematics.

Linear transformations, their range and rank, and projection operators.

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Question from the DSE 2015 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.