Further maths help

One way to not remember all the transformation matrices is to recall

is the same thing as saying "The matrix maps (transforms) the vector $\begin{bmatrix} 1 \\ 0 \end{bmatrix}$ to $\begin{bmatrix} a \\ b \end{bmatrix}$". Similar for $\begin{bmatrix} 0 \\ 1 \end{bmatrix}$.

So you have two very easy test vectors to check whether your transformation matrix makes sense. Or in reality, you have the two vectors to reconstruct the transformation matrix.

Say for instance, you don't know what the matrix for rotation by 90 degrees (anticlockwise) is. Well, we know $\begin{bmatrix} 1 \\ 0 \end{bmatrix}$ should go to $\begin{bmatrix} 0 \\ 1 \end{bmatrix}$, and $\begin{bmatrix} 0 \\ 1 \end{bmatrix}$ should go to $\begin{bmatrix} -1 \\ 0 \end{bmatrix}$. There you go, the matrix is $\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$.

Wow thank you so much! in the exam will i be expected to derive these? can I use the test vectors (1,0) and (0,1) to find the other transformations?

Hi im currently in a gap year self studying the whole of A level further maths. Im currently on chapter 7 Linear transformations and finding the derivations of the matrices quite difficult. Are the transformations given in the exam, or are we supposed to remember transformations like reflections in axis, or rotations?

Wow thank you so much! in the exam will i be expected to derive these? can I use the test vectors (1,0) and (0,1) to find the other transformations?

I was in a similar position to you and I'd really recommend Mr Bicen on YouTube because the textbooks are rubbish and miss a lot out. His videos are pretty much lessons on every topic and optional modules.

These are base vectors (1,0) and (0,1) and you should know how to construct the required transformation.
Are you using Dr Frost?

No, ive just been working through the chapters in the textbook. As well as watching Bicen maths for parts i dont understand. I have had a look at dr frost, but all i have found is some powerpoint presentations which I havent found particularly useful.