Matrices

Point p is transformed by the matrix $\begin{pmatrix} 3 & 1 \\6 & 3 \end{pmatrix}$
Followed by a further transformation by the matrix $\begin{pmatrix} -2 & 1 \\0 & -1 \end{pmatrix}$

a) Work out the matrix for the combined transformation
(I've done this bit) I got $\begin{pmatrix} 0 & 1 \\-6 & -3 \end{pmatrix}$
b) The imagine of point P after the combined transformation is (2,3). Work out the co-ordinates of P. Confused on this.
Exam is tomorrow aarrhh

Point p is transformed by the matrix $\begin{pmatrix} 3 & 1 \\6 & 3 \end{pmatrix}$
Followed by a further transformation by the matrix $\begin{pmatrix} -2 & 1 \\0 & -1 \end{pmatrix}$

a) Work out the matrix for the combined transformation
(I've done this bit) I got $\begin{pmatrix} 0 & 1 \\-6 & -3 \end{pmatrix}$
b) The imagine of point P after the combined transformation is (2,3). Work out the co-ordinates of P. Confused on this.
Exam is tomorrow aarrhh

If P has been transformed by that matrix, then we can write
$[br]\begin{pmatrix}[br]0 & 1\\ [br]-6 & -3[br]\end{pmatrix}\begin{pmatrix}[br]x\\ [br]y[br]\end{pmatrix}=\begin{pmatrix}[br]2\\ [br]3[br]\end{pmatrix}[br]$

We do not do inverse at level 2 FM

Not very "FM" really is it?

Not sure what you mean
Matrices are not in GCSE or even A Level

They appear for multiplication and transformation in the Level 2 FM

Then the inverse is only in the A Level Further Maths

I meant it's a bit disingenuous calling it "further" maths when it's testing less knowledge than that which used to be tested at "Ordinary" level.

Still, I'm sure there's a purpose to people collecting all these extra bits of paper for Mr Gove

Ah I see

Well, tbh the Level 2 FM is the only course I have found that tests year 11 to the standard I like - it has matrices, differentiation, quite a bit of co-ord geometry - it certainly takes them "further" than the GCSE


Oh, and you are showing your age - matrices are out when I did my O'levels - or maybe you just did London Board - I believe they kept them in forever

I did SMP Modern Maths O level in the early 1980s and we covered groups, matrices, sets, different number bases, modular arithmetic and Euler's formula in topology, so we knew all about "inverses", "identity", "associativity" etc for O level. In fact, we did addition and multiplication of different sized rectangular matrices at middle school when I was about 12 years old (!), but we didn't cover inverses of 2x2 until I got up to High School where we used matrices both for transformations and solving simultaneous eqs in 2 variables