Factorising determinantsAQA A-Level Further Maths: Flashcards

What these 12 flashcards ask

What does adding a multiple of one row to another do to a determinant?
What happens to a determinant when two rows are swapped?
A determinant has two identical columns. What is its value?
If row 2 of a determinant is multiplied by k, what happens to the determinant?
How do you take a common factor out of a determinant?
Which operation shows (x+2) is a factor of \begin{vmatrix} x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x \end{vmatrix}?
Why is (x-k) a factor if two columns become identical when x=k?
Why create zeros before expanding a determinant?
What sign pattern is used when expanding a 3\times3 determinant?
Value of \begin{vmatrix} 1 & 1 & 1 \\ a & b & c \\ a^2 & b^2 & c^2 \end{vmatrix}?
Why must you not use R1\to 2R1+R2 when simplifying?
How can you check a factorised determinant of degree 3?

Exam questions on Factorising determinants

Let $\Delta=\begin{vmatrix} x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x \end{vmatrix}$ .
Use a column operation to show that $(x+2)$ is a factor of $\Delta$ .2 marks
Let $\Delta=\begin{vmatrix} 1 & 1 & 1 \\ x & 2 & 3 \\ x^2 & 4 & 9 \end{vmatrix}$ .
Explain why $(x-2)$ is a factor of $\Delta$ .2 marks
Let $\Delta=\begin{vmatrix} x+1 & 2 & 3 \\ 1 & x+2 & 3 \\ 1 & 2 & x+3 \end{vmatrix}$ .
Show that $(x+6)$ is a factor of $\Delta$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).