Back to the full dot-point answer
SingaporeFurther MathsQuick questions
Matrices and Linear Spaces
Quick questions on Linear spaces explained: H2 Further Mathematics
4short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is rank of a matrix?Show answer
The rank of a matrix is the number of linearly independent columns (equivalently independent rows), found by reducing to row-echelon form and counting the non-zero rows. It is the dimension of the column space, the subspace spanned by the columns.
What is q1?Show answer
State the condition for vectors to be linearly independent. [2 marks]
What is q2?Show answer
A -column matrix has rank . State its nullity. [1 mark]
What is q3?Show answer
Why is a line not passing through the origin not a subspace? [2 marks]
Have a question we have not covered?
This dot-point answer is short enough that we have not extracted many short questions yet. Read the full dot-point answer or ask Mo, our study assistant, in the chat for follow ups.