• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Matrix power. The internal assessment will focused on observing patterns of matrix powers which will be the main key to find the general expression of matrix powers.

Extracts from this document...

Introduction

Internal Assessment- Matrix Powers

The internal assessment will focused on observing patterns of matrix powers which will be the main key to find the general expression of matrix powers.   1)

Explanation: When matrix M is powered by 2 it gives a result of from GDC, when M is powered by 3 it gives a result of from GDC and when M is powered by 4 it gives a result of from GDC. The pattern shown is that every time M is powered by a number after its preceding number it is multiply by 2. For instance, 4 shown in matrix , 8 shown in matrix , and 16 shown in matrix . Thus, these results make a general expression that . This formula is proven correct because when Middle such as 7 when n = 3, 9 when n = 4 and then 31 when n = 5. Thus, these results make a general expression that . This formula is proven correct because when from GDC and this formula also works when from GDC.   Explanation: When matrix S is powered by 3 it gives a result of from GDC, when matrix S is powered by 4 it gives a result of from GDC, and when matrix S is powered by 5 it gives a result of from GDC. The pattern shown is that results have a common factor of such as 4 shown in matrix , 8 shown in matrix , and then16 shown in matrix . Once the resulting matrix is factor out, the

Conclusion is equivalent to result matrix , where as the results of is equivalent to result matrix and the results of is equivalent to result matrix . The pattern also shows that when the matrix formula is , when the matrix formula is , and when the matrix formula is . This shows that any number representing corresponds to and . Thus, these results give a general expression that . For instance, if and then = from GDC.

4)

Explanation: After a further investigation with further values of k and n, the results shows that the limitation for n is that all negative numbers and non-integers value because when a matrix is powered by negative numbers or non-integers value the calculator gives a math error text. In addition there’s no limitation for k.

5)

In conclusion,

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related International Baccalaureate Maths essays

1. ## Extended Essay- Math

jxR0ï¿½)ï¿½^ï¿½ï¿½ï¿½ï¿½aï¿½oï¿½ï¿½ï¿½ï¿½'/ï¿½ï¿½oï¿½3/4ï¿½kï¿½Tï¿½ï¿½(r)ï¿½D"}ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½" -ï¿½0-356(c)lï¿½Ü²qbÐ¸ï¿½3/4ï¿½tï¿½h`gï¿½ï¿½ï¿½Óï¿½ï¿½.?ï¿½ï¿½ ï¿½vï¿½Zï¿½uï¿½Rï¿½""ï¿½fÍQï¿½h}ï¿½T i"ï¿½ ï¿½ï¿½ï¿½ï¿½J(ï¿½hï¿½ ï¿½gï¿½ï¿½"ï¿½KWï¿½ï¿½ï¿½ "Q0ï¿½'(r)ï¿½ k-ï¿½Pï¿½ï¿½ï¿½×·ï¿½VM-1ï¿½"ï¿½ï¿½"Zï¿½(r)mj-ï¿½ï¿½cï¿½^:ï¿½ï¿½\-ï¿½ï¿½*ï¿½9)ï¿½7o-Y6(c)%-- /i3/4Sï¿½Îï¿½Mgï¿½ IG%Ûµ-,Zï¿½0ï¿½ï¿½ï¿½'1/4I7ï¿½@"ï¿½ï¿½ï¿½2ïï¿½Pï¿½j5hï¿½ ï¿½-ï¿½hiË¿ï¿½(c)eï¿½5ï¿½ï¿½|Mï¿½pKcG ?""@ï¿½f1peï¿½ï¿½ï¿½ï¿½ï¿½ï¿½f%!rï¿½ï¿½ï¿½qï¿½ï¿½ Yï¿½f'Å­Ú¡ï¿½ï¿½N-(-ï¿½ï¿½zï¿½ï¿½VTï¿½'Mï¿½ï¿½)ï¿½"ï¿½ì"Pï¿½(tm)ï¿½ï¿½ï¿½-ï¿½Éï¿½bï¿½J8ï¿½>"d'bï¿½S(tm)` nï¿½ï¿½ï¿½&ï¿½PYï¿½ï¿½u Rï¿½Óï¿½ï¿½â(% ï¿½\$%% :T"4ï¿½+rzC'ï¿½e=Gï¿½ï¿½ï¿½b{4tÐ±ï¿½4ï¿½)ï¿½ï¿½mï¿½ppï¿½lï¿½bO(Øï¿½sï¿½ -ï¿½JnhOt|ï¿½ï¿½ï¿½J-P}ï¿½ ï¿½ï¿½eï¿½ï¿½8ï¿½ï¿½ï¿½ï¿½ë-ï¿½ï¿½ï¿½ï¿½ï¿½" ï¿½+ÂPï¿½ï¿½8ï¿½w}ï¿½Mï¿½ï¿½}ï¿½ï¿½ï¿½ï¿½ï¿½Kï¿½ï¿½ï¿½[ï¿½ï¿½""ï¿½ï¿½wï¿½EIï¿½}ï¿½AVï¿½ï¿½zï¿½ï¿½/ï¿½ï¿½ï¿½"W/Pp_ï¿½ï¿½ï¿½#(tm)...ï¿½z1/4ï¿½ï¿½=ï¿½3/4ï¿½ï¿½CoRK"/ï¿½zpï¿½ï¿½8\$(c)]"Rï¿½"ï¿½aï¿½h5dï¿½ ;W~ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½Q Lcï¿½9ï¿½ï¿½×£ï¿½ï¿½ï¿½ ï¿½Ñ¸ï¿½ï¿½Dï¿½D\ï¿½%ï¿½Xï¿½ W ï¿½<.-xï¿½'^ï¿½\$ï¿½ï¿½;ï¿½ï¿½ï¿½ Rï¿½ï¿½ï¿½Ö³ï¿½~ï¿½}ï¿½ ï¿½ï¿½'Jï¿½qï¿½ï¿½ &ï¿½"ï¿½ !3/4ï¿½<ï¿½+1/4ï¿½"ï¿½Kï¿½oï¿½j-qï¿½ï¿½Jï¿½ï¿½?ï¿½ï¿½q)ï¿½ï¿½ ï¿½zï¿½Wï¿½1ï¿½<x^eï¿½ ...ï¿½z--1/2ï¿½ï¿½(c)cï¿½v "ï¿½Tï¿½ï¿½ï¿½ï¿½ iIDATï¿½8ï¿½b*1/2ï¿½ï¿½ï¿½X<vppï¿½ï¿½Ì¬2ï¿½/JJJ ï¿½1/2Ùï¿½y-i ï¿½;ï¿½5ï¿½1/4ï¿½ï¿½ï¿½íï¿½ï¿½ ^ï¿½ï¿½D-m7 KBï¿½ "ï¿½&ï¿½ï¿½0 ï¿½ï¿½ï¿½ï¿½1/2 (tm)'ï¿½ï¿½ =kï¿½"kï¿½\ï¿½ï¿½ drFï¿½)ï¿½ï¿½ï¿½ï¿½F'g7 KBï¿½rï¿½ ,+5Å£6Dï¿½)Y|Ð@C 4ï¿½ï¿½cKï¿½_3ï¿½ ï¿½Eï¿½ï¿½Fï¿½ï¿½Aï¿½(r)ï¿½\$,ï¿½|Gï¿½Yï¿½ï¿½ï¿½ï¿½ï¿½.1/2"ï¿½ Bjï¿½2ztï¿½tï¿½ç}kRï¿½ï¿½hï¿½_zï¿½ï¿½Kï¿½k-"rï¿½ï¿½ (c)%ï¿½ï¿½uï¿½nVï¿½mï¿½ï¿½BZï¿½ Ù¥ï¿½Ë­,9<'\("ZT-"ï¿½(QIPï¿½'1/2 1/4ï¿½ZHï¿½<ï¿½ï¿½j:3/4ï¿½V""uï¿½ï¿½ï¿½ï¿½ï¿½(tm)ï¿½*-[ï¿½1/4pï¿½ÔeF(Xï¿½ï¿½4ï¿½-}ï¿½"s "(c)Gï¿½3ï¿½Gï¿½ï¿½ï¿½~8MFJ)Pï¿½"ï¿½ï¿½πï¿½ï¿½(tm)

2. ## Maths Internal Assessment -triangular and stellar numbers

there would be the need to write out the sequential sum for the further layers. Secondly, the knowledge of the triangular shapes was also applied to the creation of the 6-stellar numbers to discover the connection between the number of dots and the layers.

1. ## Stellar Numbers. After establishing the general formula for the triangular numbers, stellar (star) shapes ...

+ 1 U5 = 3(25) - 15 + 1 U5 = 75 - 14 U5 = 61 The results derived from the general formula are the same as worked out earlier when not applying any formula at all; hence, it is correct and can be applied to terms 3 and 5.

2. ## matrix power

However, for a matrix to be able to be raised to the power the matrix must be a square matrix, meaning that it must be orthogonal in shape and contains the same width and height all around. The following list describes the effects on a matrix when a matrix is

1. ## Math IA - Matrix Binomials

(a=10): Using all three values of constant a (2, -2, and 10), we have arrived at a general equation. However, we must note that this formula only gives us the progression for the scalar values which will be multiplied to the matrix, A.

2. ## This essay will examine theoretical and experimental probability in relation to the Korean card ...

x (15/19) x (1/18) x 17/17) = 1/228 P(all) = (1/1292) + (1/228) = 5/969 Probability of winning with September (Ddaeng-9) is split into three different possibilities. First one is when player 2 has one card that has?, second one is when player 2 does not have? and does have October and last one is when player 2 does not have both?

1. ## Infinite Summation Internal Assessment ...

Examining the table, increases quickly until the value of is about 4, where the value of continues to stay in the range of 7 never reaching 8, since the horizontal asymptote is 8.

2. ## IB Math Methods SL: Internal Assessment on Gold Medal Heights

function and the linear function (reproduced below): Information Table 2 (Table of values from linear equation y = 1.02x + 187) Years Elapsed (t) 0 4 8* 12* 16 20 24 28 32 36 40 44 48 Height in cm (h) • Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to 