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

Matrices Portfolio

Extracts from this document...

Introduction

Matrix powers

A matrix is a rectangular array of numbers (or letters) arranged in rows and columns. These numbers (or letters) are known as entries. Entries can be added and multiplied, but also squared. The aim of this portfolio is to investigate squaring matrices.

When we square the matrix M =  what we receive is a)  =  =  .

Calculating the matrices for n = 3, 4, 5, 10, 20 and 50:  =    =    =    =    =    =  Examples shown above clearly indicate that while zero entries remain the same, non-zero entries change. Each entry is raised to a given power separately. Raising them to any power does not change the zero-entries.

Middle These matrices are simplified to 2  and 2  to make it easier to notice any patterns. Calculating Pn and Sn

Conclusion

k and n it occurred, that for greater numbers the pattern was not true. In the case of, e.g. k = 1500 and n = 2, the pattern worked. Increasing n to 3, however, caused all the entries to be the same.

This was also checked for the matrices P and S.  =  =  = 65536    =  =    =  =  = 4096    =  =  The pattern works as long as the results are less than 10 billions. If they exceed this number, all the entries will be exactly the same.  10 000 000 000

Therefore, this does not seem to be true for every number.

The results hold true in general because in real life situations so large numbers are not frequently used. For smaller numbers the pattern fits thoroughly.

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. Math IA binomials portfolio. As we can see, a general trend emerges as we ...

We can find an expression for Yn in a similar fashion. , where Un=a specific term a=first term r=common ratio (multiplier between the entries of the geometric sequence) n=the number of the specific term (with relation to the rest of the sequence). For Yn: When n=1, 2, 3, 4, ...

2. Math Portfolio: trigonometry investigation (circle trig)

and y=cos? for the domains -???. The sin? graph passes through the points (-,0), (-,1), (-,0), (-,-1), (0,0), (,1), (,0), (,-1), and (,0) with 9 coordinates as seen in the graph above. Upon the analysis of the pattern of the graph, As the value of ?

1. matrix power

To enter a matrix into a Ti-83 Graphing calculator we would need to follow the following steps. In order to enter the matrix into the Ti-83, press the [MATRIX] key, select [EDIT] and then [MATRIX A]. Next, enter the order of the matrix, in this case the matrix has a

2. Math portfolio: Modeling a functional building The task is to design a roof ...

to the volume of the office block for each height mentioned above. Volume of the waste space= volume of the structure - volume of the office block Volume of the office block= height � length � width =0.67H � 150 � 41.56 = 4176.78H The volume of the structure= length

1. Math Portfolio Type II

Part 5 Let us see what happens when the initial growth rate is 2.9 The ordered pair (u0, r0) for the first pair when the predicted growth rate 'r' for the year is 2 will be (10000, 2.9). (un, rn)

2. Maths Project. Statistical Analysis of GCSE results at my secondary school summer 2010 ...

183 Ar 9 40 40 f 80 182 Ba 9 40 46 f 86 181 Ba 8 52 52 f 104 180 Ba 10 46 40 f 86 179 Be 11 40 40 f 80 178 Be 10 40 46 m 86 177 Bi 10 40 28 m 68 176

1. Math 20 Portfolio: Matrix

Considering the follow arrays of rectangular diagrams shown below: In each diagram, there are two copies of the triangular diagram, a black one and a white one. The original triangular diagrams from stage 1 to stage 8 now transformed into rectangles.

2. Math HL portfolio

which is shown in the graph below: 3. Investigate your conjecture for any real value of a and any placement of the vertex. Refine your conjecture as necessary and prove it. Maintain the labelling convention used in parts 1 and 2 by having the intersections of the first line to be and , and the intersections with the second line to be and . • Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to
improve your own work 