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Questions › DSE › DSE 2008 › Q16
1 markMathematics › Vector spaces, rank and eigenvalues › Linear maps, rank and projectionsModerateabout 2 min

DSE 2008 Question 16: Vector spaces, rank and eigenvalues

Consider two functions mapping points on the plane back to points on the plane: (i) f(x1,x2)=(x1+1, x2+1)f(x_{1},x_{2})=(x_{1}+1,\ x_{2}+1)f(x1​,x2​)=(x1​+1, x2​+1) and (ii) g(x1,x2)=(x2,x1)g(x_{1},x_{2})=(x_{2},x_{1})g(x1​,x2​)=(x2​,x1​). Which of the above functions is a linear function?

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Consider two functions mapping points on the plane back to points on the plane: (i) f(x₁,x₂)=(x₁+1, x₂+1) and (ii) g(x₁,x₂)=(x₂,x₁). Which of the above functions is a linear function? (A) Both functions are linear. (B) Neither function is linear. (C) f is a linear function, g is not linear. (D) g is a linear function, f is not linear.

Also written as: Consider two functions mapping points on the plane back to points on the plane: (i) f(x_1,x_2)=(x_1+1, x_2+1) and (ii) g(x_1,x_2)=(x_2,x_1). Which of the above functions is a linear function?

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.

TestStop has 14 past-paper questions on this subtopic.

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Question from the DSE 2008 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.