FP1 questions (matrices and coordinate geometry)
I can can do part a in both questions, Im just stuck on how to do part b
Original post by creativebuzz
I can can do part a in both questions, Im just stuck on how to do part b
I can can do part a in both questions, Im just stuck on how to do part b
Which 2 questions is it, there's 9, 10 and 11. . .
Original post by creativebuzz
I can can do part a in both questions, Im just stuck on how to do part b
I can can do part a in both questions, Im just stuck on how to do part b
One of us can't count - I can see 3 questions
For 10(b), if L = MN for general matrices L,M and N, what is the inverse of L in terms of M and N? You have all the ingredients to answer (b) from part (a)
For Question 9, you need to form the equation of the line PQ. You can then substitute in coordinates and the given equality pq = -1 will follow naturally.
For question 10, you'll need to manipulate the expression C = AB first, remembering the important facts that MM^-1 = I for any matrix M, and also MI = M. You can then express B^-1 in terms of the matrices you already know.
I assumed it was those two questions you were referring to but in case, for question 11 part b it would be helpful to draw the identity matrix and the transformation matrix in order to visualise what's happening under the transformation. It basically comes down to knowing the geometrical significance of root(2)/2; I think such transformations may sometimes be given in formula booklets anyway though.
For question 10, you'll need to manipulate the expression C = AB first, remembering the important facts that MM^-1 = I for any matrix M, and also MI = M. You can then express B^-1 in terms of the matrices you already know.
I assumed it was those two questions you were referring to but in case, for question 11 part b it would be helpful to draw the identity matrix and the transformation matrix in order to visualise what's happening under the transformation. It basically comes down to knowing the geometrical significance of root(2)/2; I think such transformations may sometimes be given in formula booklets anyway though.
(edited 9 years ago)
Original post by davros
One of us can't count - I can see 3 questions
For 10(b), if L = MN for general matrices L,M and N, what is the inverse of L in terms of M and N? You have all the ingredients to answer (b) from part (a)
For 10(b), if L = MN for general matrices L,M and N, what is the inverse of L in terms of M and N? You have all the ingredients to answer (b) from part (a)
Apologies, I said both because I upload two pictures which I assumed had one question on each screenshot
Original post by 1 8 13 20 42
For Question 9, you need to form the equation of the line PQ. You can then substitute in coordinates and the given equality pq = -1 will follow naturally.
For question 10, you'll need to manipulate the expression C = AB first, remembering the important facts that MM^-1 = I for any matrix M, and also MI = M. You can then express B^-1 in terms of the matrices you already know.
I assumed it was those two questions you were referring to but in case, for question 11 part b it would be helpful to draw the identity matrix and the transformation matrix in order to visualise what's happening under the transformation. It basically comes down to knowing the geometrical significance of root(2)/2; I think such transformations may sometimes be given in formula booklets anyway though.
For question 10, you'll need to manipulate the expression C = AB first, remembering the important facts that MM^-1 = I for any matrix M, and also MI = M. You can then express B^-1 in terms of the matrices you already know.
I assumed it was those two questions you were referring to but in case, for question 11 part b it would be helpful to draw the identity matrix and the transformation matrix in order to visualise what's happening under the transformation. It basically comes down to knowing the geometrical significance of root(2)/2; I think such transformations may sometimes be given in formula booklets anyway though.
I don't actually have the answer for q10 but I managed to get
7 10
-1/2 1
Is that incorrect?
Original post by 1 8 13 20 42
For Question 9, you need to form the equation of the line PQ. You can then substitute in coordinates and the given equality pq = -1 will follow naturally.
For question 10, you'll need to manipulate the expression C = AB first, remembering the important facts that MM^-1 = I for any matrix M, and also MI = M. You can then express B^-1 in terms of the matrices you already know.
I assumed it was those two questions you were referring to but in case, for question 11 part b it would be helpful to draw the identity matrix and the transformation matrix in order to visualise what's happening under the transformation. It basically comes down to knowing the geometrical significance of root(2)/2; I think such transformations may sometimes be given in formula booklets anyway though.
For question 10, you'll need to manipulate the expression C = AB first, remembering the important facts that MM^-1 = I for any matrix M, and also MI = M. You can then express B^-1 in terms of the matrices you already know.
I assumed it was those two questions you were referring to but in case, for question 11 part b it would be helpful to draw the identity matrix and the transformation matrix in order to visualise what's happening under the transformation. It basically comes down to knowing the geometrical significance of root(2)/2; I think such transformations may sometimes be given in formula booklets anyway though.
As for question 9, Ive seemed to have gotten stuck, this is what I have done so far:
Original post by creativebuzz
As for question 9, Ive seemed to have gotten stuck, this is what I have done so far:
I can't really check the matrices thing right now but as for this one, you basically just want to repeat what you've done there for the line PQ. Instead of using dy/dx for the gradient, you will have to use the coordinates of P and Q to find it (a bit of factorisation is probably advisable to get it in a manageable form). Once you have found the equation of that line, you can substitute in the coordinates of the focus.
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