Simple Matrix Question Watch

etp
Badges: 11
Rep:
?
#1
Report Thread starter 10 years ago
#1


M = \[\begin{pmatrix}a & c \\ b & d\end{pmatrix}\]

Find M^2 and express it in the form of M thus find a formula that gives M^n in the form of M.

Heres what I got:



\[\begin{pmatrix}a & c \\ b & d\end{pmatrix}\]\times\begin{pmatrix}a & c \\ b & d\end{pmatrix}

= \[\begin{pmatrix}a^2 + cb & ac + dc \\ ba + db & ab+db\end{pmatrix}\]

I didn't know where to go from there, but the book says:

M^2 = (a + d)M

so I multiplied it out to see where mine differs:

(a + d)M = \[\begin{pmatrix}a^2 + da & ac + dc \\ ab+db & ad+d^2\end{pmatrix}\]

so M_{21} and M_{12} are correct - but where did I go wrong?
0
reply
DFranklin
Badges: 18
Rep:
?
#2
Report 10 years ago
#2
For a general 2x2 matrix, M^2 \neq (a+d)M. Are you sure there weren't some extra conditions on M (or a,b,c,d)?
0
reply
etp
Badges: 11
Rep:
?
#3
Report Thread starter 10 years ago
#3
A 2 \times 2 singular Matrix M is given as \begin{pmatrix}a & c \\ b & d\end{pmatrix}.
Find M^2 and give your answer as a multiple of M.
Hence find a formula which gives M^n in terms of M.
Is the question word for word from the MEI FP1 book.
0
reply
SsEe
Badges: 13
Rep:
?
#4
Report 10 years ago
#4
I see the word "singular" has cropped up. ie, the determinant (ad-bc) is zero. Try and use that.
0
reply
etp
Badges: 11
Rep:
?
#5
Report Thread starter 10 years ago
#5
ah doh, ad = bc thanks!
0
reply
etp
Badges: 11
Rep:
?
#6
Report Thread starter 10 years ago
#6
Another question, this time I have no idea:

A shear moves each point parallel to the line y = mx.
Each point is moved p times its distance from the line y = mx.
(Points to the right of the line are moved upwards, points to the left of the line are moved downwards).

I(1,0) J(0,1) - Find I` and J` thus find the matrix representing this shear.

So I drew a simple diagram:



Any tips on where to start?
0
reply
Vjyrik
Badges: 10
Rep:
?
#7
Report 10 years ago
#7
(Original post by etp)
Another question, this time I have no idea:

A shear moves each point parallel to the line y = mx.
Each point is moved p times its distance from the line y = mx.
(Points to the right of the line are moved upwards, points to the left of the line are moved downwards).

I(1,0) J(0,1) - Find I` and J` thus find the matrix representing this shear.

So I drew a simple diagram:



Any tips on where to start?
I'd write it out as a set of simultaneous equations, firstly. I'm trying to do it, but don't expect any results :p:
0
reply
etp
Badges: 11
Rep:
?
#8
Report Thread starter 10 years ago
#8
I found it out by have a vector-parametric equation, but i guess theres a simpler version but I had no idea :s
0
reply
Vjyrik
Badges: 10
Rep:
?
#9
Report 10 years ago
#9
(Original post by etp)
I found it out by have a vector-parametric equation, but i guess theres a simpler version but I had no idea :s
Meh, I got lazy -> http://en.wikipedia.org/wiki/Shear_mapping

I think it is just something you ought to know by heart when you come into the exam. I didn't :rolleyes:.

Can you tell me the exercise number? I never managed to do the shears, cause they're such a *****. :mad:
0
reply
etp
Badges: 11
Rep:
?
#10
Report Thread starter 10 years ago
#10
1F - Q9.

If that came up in the exam I'd have no hope in hell, I just thought i'd try the question in vector form and it worked. I think the questions in the book are quite taxing, how do they compare to exam questions?
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • Cardiff Metropolitan University
    Undergraduate Open Day - Llandaff Campus Undergraduate
    Sat, 27 Apr '19
  • University of East Anglia
    Could you inspire the next generation? Find out more about becoming a Primary teacher with UEAโ€ฆ Postgraduate
    Sat, 27 Apr '19
  • Anglia Ruskin University
    Health, Education, Medicine and Social Care; Arts, Humanities and Social Sciences; Business and Law; Science and Engineering Undergraduate
    Sat, 27 Apr '19

Have you registered to vote?

Yes! (571)
37.71%
No - but I will (119)
7.86%
No - I don't want to (109)
7.2%
No - I can't vote (<18, not in UK, etc) (715)
47.23%

Watched Threads

View All