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Questions › DSE › DSE 2015 › Q10
1 mark, −0.333333333333333Mathematics › Vector spaces, rank and eigenvalues › Linear maps, rank and projectionsModerateabout 3 min

DSE 2015 Question 10: Vector spaces, rank and eigenvalues

Let F:R2→R2F:\mathbb{R}^2\to\mathbb{R}^2F:R2→R2 be linear with F(1,2)=(2,3)F(1,2)=(2,3)F(1,2)=(2,3) and F(0,1)=(1,4)F(0,1)=(1,4)F(0,1)=(1,4). Then in general F(x1,x2)F(x_1,x_2)F(x1​,x2​) equals

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Let F:ℝ²→ℝ² be linear with F(1,2)=(2,3) and F(0,1)=(1,4). Then in general F(x₁,x₂) equals (A) (x₂, 4x₂) (B) (x₂, x₁+x₂) (C) (1+x₁, 4x₂) (D) (x₂, -5x₁+4x₂)

Also written as: Let F:R^2->R^2 be linear with F(1,2)=(2,3) and F(0,1)=(1,4). Then in general F(x_1,x_2) equals

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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Practise Vector spaces, rank and eigenvaluesMore on Linear maps, rank and projections

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