Scalar Multiplication in Determinant and Matrices

The study of determinants and matrices can be confusing at time. They look almost the same, and are closely related. As such, some mathematical operations on them are similar.

But, there are differ somewhat and have to be taken care of.

Below is one such mistake that is often made by learning math students.



The upper row involves matrices. The scalar multiplication of it by "a" affects ALL the elements within the matrix.

For the lower row, the scalar "a" multiplication affects only one column (or one row) of the determinant.

Just note this different and commit it to memory. This is good for you and can save you a lot of further troubles with matrix and determinant.

So, just simply identifying the differences between matrices and determinant, in term of their operations, you will be enjoying them for a long time.

With less mistake made, you will be more gear towards doing a better job out of maths. This is human nature.

Cheers! and Happy mathematics!
:D

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!
:-)