Matriks | Lectures

Good Night friends my loyal blog…..

In this post I will share knowledge matrix subject, I hope this post can make reference to you

Metrics is a collection of rectangular numbers arranged in rows and columns. Numbers contained in a matrix called the elements or members of the matrix. With the representation of matrix, the calculation can be done with more structured. Utilization for example in explaining linear equations, coordinate transformations, and more. Matrix as well as ordinary variables can be manipulated, such as multiply, add up, deductible and decomposed.

Design of Matriks

operations on matrix operations

a. Addition and Reduction matrix, valid for matrices sized same.

If metrics A = and B = same size, and then :

A + B = C where C= ; ; For every i and j.

Example 1:

A =

B =

The equals :

A + B =……

A – B =……

b. Against Metrics Scalar Multiplication

If k scalar and A = is metrics and then kA=

Contoh:

A = and k= and then kA =

Some Laws in addition and scalar multiplication, if A, B and C are the same ordo matrix, and k scalar then:

1. A+B = B+A (Komutatif)

2. (A+B)+C = A+(B+C) (Assosiatif)

3. k(A+B) = kA + kB (Distributif)

2.c. multiple Metrics

reqruitment:

The number of first matrix column = number of second matrix row.
If A = (aij) measuring pxq
And B = (bij) measuring QXR
Then multiplication A x B = C, wherein C = (CIJ) measuring PXR
for every i = 1,2, ..., p and j = 1,2, ..., r

Example:

A= ; B=

and then AB=

=

BA = ……..?

BA matrix can not be completed because the number of columns the matrix B is not equal to the number of rows in the matrix A.

The properties that apply to matrix multiplication, if A, B, C is the matrix multiplication matrix qualified, are:
AB ≠ BA (does not meet the commutativity)
A (B + C) = AB + AC (distributive properties)
A (BC) = (AB) C (associative)

I would ask you to do the problems below…

1. If known A= and B= look and

A_2x3 B_3x1 and then AB_2x1

AB = and …….????