University vector spaces and linear maps quiz to download as PDF

This University vector spaces and linear maps quiz has 10 short questions for pupils aged 18-19. Type your answer, check it straight away and read the explanation when you get one wrong.

University vector spaces and linear maps quiz: the 10 questions

Dimension of the plane \(x+y+z=0\)?
\(\dim P_3\)?
Nullity if rank is 2 and the domain is \(\mathbb R^5\)?
Are \((1,2)\) and \((2,4)\) independent?
Does a subspace contain the zero vector?
Kernel of \(T(x,y)=(x,0)\)?
Is \(x\mapsto x^2\) a linear map \(\mathbb R\to\mathbb R\)?
Number of vectors in a basis of \(\mathbb R^3\)?
Image of the identity map on \(V\)?
Rank-nullity theorem: rank + nullity equals what?

How to use this University vector spaces and linear maps quiz

First, answer every question without a calculator unless the question says so. Then check your answer and read the short explanation. If you get fewer than 7 right, revise the vector spaces and linear maps lesson and try again later. After that, try the multiple choice questions or the vector spaces and linear maps worksheet.

Finally, take this quiz again before a test, because quick retrieval helps you remember. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.