"Live as if you were to die tomorrow. Learn as if you were to live forever." - Mahatma Gandhi

Definition of Row-Echelon of a Matrix

A matrix in row-echelon form has the following properties.

1. All rows consisting entirely of zeros occur at the bottom of the matrix.
2. For each row that does not consist entirely of zeros, the first nonzero entry is 1.
3. For two successive (nonzero) rows, the leading 1 in the higher row is farther to the left than the leading 1 in the lower row.

a.   1   2   -1   4                                    b.    1   -5   2   -1   3
      0   1   0    3                                            0   0   1    3   -2
      0   0   1   -2                                            0   0   0    1    4
                                                                     0   0   0    0    1


Reduced Row-Echelon

a.     0   1   0   5                                    b.    1   0   0   -1
        0   0   1   3                                           0   1   0   2
        0   0   0   0                                           0   0    1   3
                                                                    0   0   0    0

Elementary Row Operations

1. Interchange two equations.
2. Multiply an equation by a nonzero constant.
3. Add a multiple of an equation to another constant.

Two matrices are said to be row-equivalent if one can be obtained from the other by a finite sequence of elementary row operations.

Example:

a. Interchange the first and second rows.

          Original Matrix                                New Row-Equivalent Matrix

                      0   1   3   4                                            -1   2   0   3
                      -1   2   0   3                                           0   1   3   4
                      2   -3   4   1                                           2   -3   4   1

 

b. Multiply the first and second row by 1/2 to produce a new first row.

                    Original Matrix                                      New Row-Equivalent Matrix
                   
                     2   -4   6   -2                                                 1   -2   3   -1
                     1   3   -3   0                                                   1   3   -3   0
                     5   -2   1    2                                                  5   -2   1   2

c. Add -2 times the first row to the third row to produce a new third row.

                    Original Matrix                                       New Row-Equivalent Matrix

                      1   2   -4    3                                               1   2   -4   3
                      0   3   -2   -1                                               0   3   -2   -1
                      2   1    5    -2                                              0   -3   13   -8

MATRICES

Nakakalito at times.

The image above is an exmaple of MATRIX. Wait, ano nga ba ang matrix?

- A matrix is a rectangular array in which each entry, of the matrix is a number. 

Other terms:

• Real Matrix - If each entry of a matrix is a real number, then the matrix is called a real matrix. 
• Row Subscript - it identifies the row in which the entry lies. ( index i )
• Column Subscript - it identifies the column in which the entry lies. ( index j )

A matrix with m rows and n columns ( an m x n ) is said to be of size m x n. If m = n, the matrix is called square of order n. For a square matrix, the entries a11, a22, a33, ... are called the main diagonal.

Augmented Matrix

           - the matrix derived from the coefficients and constant terms of a system of linear equations.

Coeffiecient Matrix

           - the matrix containing only the coefficients of the system.

Let's have an example:

                                                        Augmented Matrix                             Coefficient Matrix

2x - 4y + 2z = 6              2   -4   2   6                            2   -4   2

-5x + 2y - z = -3             -5   2   -1   -3                          -5   2   -1 

x             - 7z = 2            1   0   -7   2                                           1   0   -7

Random thought.

Tbh, I am not a fan of blogging o ano. I'm doing this for my grades. Charr. So yea! Haha.

I'm Leia. 15. Zambales! (O dba, beauty pageant ang datingan.) I like something orange. It brings uhm happiness, energy, brightness? and other ka-ekek-an I know whenever I see things having that color. I love salad, tociyes (napakakorni), white, mint and dark chocolates. It's not obvious but just so you know, I AM A BIG FAN OF ROCK, POP, and RAP genre of music. <3 Music has been there for me. It lives byyyy.

So yea. This must be description. Pero wala eh! 
*the beat goes on and on and on and*