One of the applications of inverse matrix is in solving simultaneous equations.
If you are good with algebra, you will discover that this inverse matrix way of handling the solution of simultaneous equations is similar, except that they are done as a group, collectively.
The answers to the unknown variables are obtained at one go with this Inverse matrix method.
However, what do you need to know in order to use this Inverse matrix solving?
You have to understand:
1) Convertion of simultaneous equations into a set of matrices
2) Determinant and technique to get its numerical value
3) Minor of the individual elements within the matrix
4) Co-factor of this determinant formed with this set of matrices
5) Transpose of matrix
6) Adjoint matrix obtained with the co-factors and transposed matrix
7) Formula to relate determinant with the adjoint matrix ==> Inverse matrix
8) Matrices multiplication
The list looks amazingly long for matrix novice, but, DO NOT FEAR!
Why?
Matrices consist of numbers only, and simple mathematical operations, nothing abstract.
(The details are not presented here for fear that you will leave this site.)
Slowly research into the above terms and see for yourself that they are "friends" and not "foes".
Happy start to matrices and its application.
.
Sunday, 31 August 2008
Monday, 25 August 2008
Graphical Art (Jelly Fish)
What does the above graph looks like?A jelly fish drawn out of trigonometrical expressions. Wondering what is maths about...
Yes, on the interesting part, maths is lively, as seen above.
Animals come alive with maths.....
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Graphical Art (Volcano)
The piece of graphical art above reflects the beauty of mathematical functions when plotted.
It not only shows the trend of the equation , it can be used to draw figures.
The above diagram is drawn using trigonometrical functions, and to me, it looks like a volcano.
What do you think?
Maths is interesting, in this aspect, right?
.
Saturday, 23 August 2008
Differences between Determinants and Matrices
Determinants and matrices, they look alike. Their similarities caught many unaware and results in "excitements" and much interests.
Both contain numbers within. But ......
- determinants are bounded by two straights lines whereas matrices are by square braces
- determinant resulted in a single numerical value, whereas matrices are sets of numbers grouped within the braces
- determinant can be extracted from matrix, but not the other way round
- there are inverse matrix but not inverse determinant
- a scalar multiplier affects only a single row or single column of a determinant, but affects all the numbers within a matrix
The differences are aplenty. But those listed above are the least any maths students or person should know.
Why create such topics to excite maths learners?
Answer: So that maths will be made interesting and challenging (... the informal reply)
With open mindedness, maths is a very fantastic subject to learn and train for. It carries many hard works and beautiful thinking. Thoughts that are simple yet abstract at times.
Any more fun? ..... You are the answer!
.
Both contain numbers within. But ......
- determinants are bounded by two straights lines whereas matrices are by square braces
- determinant resulted in a single numerical value, whereas matrices are sets of numbers grouped within the braces
- determinant can be extracted from matrix, but not the other way round
- there are inverse matrix but not inverse determinant
- a scalar multiplier affects only a single row or single column of a determinant, but affects all the numbers within a matrix
The differences are aplenty. But those listed above are the least any maths students or person should know.
Why create such topics to excite maths learners?
Answer: So that maths will be made interesting and challenging (... the informal reply)
With open mindedness, maths is a very fantastic subject to learn and train for. It carries many hard works and beautiful thinking. Thoughts that are simple yet abstract at times.
Any more fun? ..... You are the answer!
.
Wednesday, 20 August 2008
Cramer and Sarrus | How are they related to maths
Cramer and Sarrus?
Who are they?
In which area of maths are they involved?
For those of you who is doing matrices, you will be familiar with their rules, I suppose.
They are famous for creating techniques used in the solution of simultaneous equations.
How so?
Cramer's Rule is a method of solving unknowns in simultaneous equations using division of various determinants.
Rule of Sarrus is a simple way of determining the numerical value of 3rd order determinant.
The two rules, therefore, complement each other to form an easy way to solve simultaneous equations.
However do note that students of these topics use to mix up the 2 rules.
When question states the use of Cramer's and Sarrus rule, they tend to get confuse. THe common notion is that Rule of Sarrus is another method to solve simultaneous equations which is not so.
It is only a technique to evaluate the determinant and get its value. It cannot solve the unknowns in the set of equations.
This is a good problem to get confuse. Why?
Getting confuse means a thinking brain and learning starts to take place. When there is no confusion, there can be two happenings.
- blank or "completely do not understand"
- "completely understood without questions"
Which is which does not matter. What is important is not to disappoint Cramer and Sarrus!
Work hard folks!
Cheers!
:-)
Who are they?
In which area of maths are they involved?
For those of you who is doing matrices, you will be familiar with their rules, I suppose.
They are famous for creating techniques used in the solution of simultaneous equations.
How so?
Cramer's Rule is a method of solving unknowns in simultaneous equations using division of various determinants.
Rule of Sarrus is a simple way of determining the numerical value of 3rd order determinant.
The two rules, therefore, complement each other to form an easy way to solve simultaneous equations.
However do note that students of these topics use to mix up the 2 rules.
When question states the use of Cramer's and Sarrus rule, they tend to get confuse. THe common notion is that Rule of Sarrus is another method to solve simultaneous equations which is not so.
It is only a technique to evaluate the determinant and get its value. It cannot solve the unknowns in the set of equations.
This is a good problem to get confuse. Why?
Getting confuse means a thinking brain and learning starts to take place. When there is no confusion, there can be two happenings.
- blank or "completely do not understand"
- "completely understood without questions"
Which is which does not matter. What is important is not to disappoint Cramer and Sarrus!
Work hard folks!
Cheers!
:-)
Tuesday, 19 August 2008
A Good Quadratic Solver
I chanced upon a good math solving tools that every math learners will love.
Even though you may not use it to solve math problems, you can take this Quadratic solver as a guide to check your answers.
It is a user-friendly tool that can give you the answer easily. Try it!
This is one of the easily available math tools that make maths learning exciting and and interesting. See for yourself.
Quadratic Solver
This solver is provided by Algebra.Com:
.
Even though you may not use it to solve math problems, you can take this Quadratic solver as a guide to check your answers.
It is a user-friendly tool that can give you the answer easily. Try it!
This is one of the easily available math tools that make maths learning exciting and and interesting. See for yourself.
Quadratic Solver
This solver is provided by Algebra.Com:
.
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