Saturday, June 28, 2014
Show respect even to those who don’t deserve it.
Not as a reflection of their character, but as a reflection of yours.
Friday, June 27, 2014
Gauss-Jordan Elimination
A method of solving a linear system of equations. This is done by transforming the system's augmented matrix into reduced row-echelon form by means of row operations.
(Click nalang link para sa meaning ng mga yan.)
(Click nalang link para sa meaning ng mga yan.)
Wednesday, June 25, 2014
Monday, June 23, 2014
Sunday, June 22, 2014
Wag kang malungkot kung palpak ang love life mo.
Sadyang matyaga lang talagang manalangin ‘yung pumapangarap sa’yo.
Imagine ALGEBRA sa public market:
"Ate sukli niyo po, x² + y +8 [(x + 2y ² = a-z] + 2x ³ + (- 2z = 2. 4) + 10y - 5Z ³= k= 9."
MATRICES
Matrix: is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
Example of a 2 x 3 matrix ("2x3" read as "two by three")
Some definition/terms about this lessons:
Matrix: is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
Real Matrix: is a matrix whose elements consist of entirely of real numbers
Augmented Matrix: is a matrix obtain by appending the columns of two given matrices, usually for the purpose of performing the same elementary row operations on the each of the given matrices.
Coefficient Matrix: refers to a matrix consisting of the coefficients of the variables in a set of linear equations.
Elementary row operation:
Rows: The horizontal line of numbers.
Columns: The vertical line of numbers.
Row Echelon form: a matrix is in echelon form if it has the shape resulting of a Gaussian elimination.
-All nonzero rows (rows with at least one nonzero element) are above any rows of all zeroes (all zero rows, if any, belong at the bottom of the matrix).
-The leading coefficient (the first nonzero number from the left, also called the pivot) of a nonzero row is always strictly to the right of the leading coefficient of the row above it (some texts add the condition that the leading coefficient must be 1.
-All entries in a column below a leading entry are zeroes (implied by the first two criteria).
Example:
![\left[ \begin{array}{ccccc}
1 & a_0 & a_1 & a_2 & a_3 \\
0 & 0 & 2 & a_4 & a_5 \\
0 & 0 & 0 & 1 & a_6
\end{array} \right]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vPSJNAcegN1fzR2m9NsuyIV9GpTlcPt7gMA3BrdEPIy9Y9FaIr5Q62fyOv3MrXf9aaE7NIFSShj0-B_Jq5Nhzt48YPknLwLio0rbmHI61gAaIi39KEQZp7cd4p2YI2eKyMzuskIgSWAkipJj0pig=s0-d)
Reduced-Row Echelon Form: A matrix is in reduced row echelon form (also called row canonical form) if it satisfies the following conditions:
-It is in row echelon form.
-Every leading coefficient is 1 and is the only nonzero entry in its column.
![\left[ \begin{array}{ccccc}
1 & 0 & a_1 & 0 & b_1 \\
0 & 1 & 0 & 0 & b_2 \\
0 & 0 & 0 & 1 & b_3
\end{array} \right]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_s6a6NR7CbbVG7KRFz5mjjIi7St80Qh-OR1wGDbd9ENswmw7quIL_x0SXS4Q6npMKafdKCSfaxsw2BNQxPvmjVhpY0am7t0RCsuA9yETu0zUSdtWoitKDvc9b-7A82f_c3YLiQ0ht8_bGHH3_u7Kw=s0-d)
Example of a 2 x 3 matrix ("2x3" read as "two by three")
Some definition/terms about this lessons:
Matrix: is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
Real Matrix: is a matrix whose elements consist of entirely of real numbers
Augmented Matrix: is a matrix obtain by appending the columns of two given matrices, usually for the purpose of performing the same elementary row operations on the each of the given matrices.
Coefficient Matrix: refers to a matrix consisting of the coefficients of the variables in a set of linear equations.
Elementary row operation:
- Interchange two of the equations in the system.
- Multiply one of the equations through by a number other than zero.
- Add a multiple of one equation to another.
Rows: The horizontal line of numbers.
Columns: The vertical line of numbers.
Row Echelon form: a matrix is in echelon form if it has the shape resulting of a Gaussian elimination.
-All nonzero rows (rows with at least one nonzero element) are above any rows of all zeroes (all zero rows, if any, belong at the bottom of the matrix).
-The leading coefficient (the first nonzero number from the left, also called the pivot) of a nonzero row is always strictly to the right of the leading coefficient of the row above it (some texts add the condition that the leading coefficient must be 1.
-All entries in a column below a leading entry are zeroes (implied by the first two criteria).
Example:
Reduced-Row Echelon Form: A matrix is in reduced row echelon form (also called row canonical form) if it satisfies the following conditions:
-It is in row echelon form.
-Every leading coefficient is 1 and is the only nonzero entry in its column.
Friday, June 20, 2014
Sunday, June 15, 2014
"An entire sea of water can’t sink a ship unless it gets inside the ship."
Similarly, the negativity of the world can’t put you down unless you allow it to get inside you.
Saturday, June 14, 2014
Friday, June 13, 2014
Ayoko:
Ayaw ko talaga mga kanta na tungkol sa sobra sa pagmamahal sa isang tao. Di muna isipin sarili. Hayy nakoo. :)
Thursday, June 12, 2014
Saturday, June 7, 2014
People get serious with their work for two reasons:
Either they want to achieve something or they have suffered a lot in their past.
Parameters
Parameter definition
A parameter is a quantity that influences the output or behavior of a mathematical object but is viewed as being held constant. Parameters are closely related to variables, and the difference is sometimes just a matter of perspective. Variables are viewed as changing while parameters typically either don't change or change more slowly. In some contexts, one can imagine performing multiple experiments, where the variables are changing through each experiment, but the parameters are held fixed during each experiment and only change between experiments.
One place parameters appear is within functions. For example, a function might a generic quadratic function as
f(x)=ax2+bx+c.
Here, the variable x is regarded as the input to the function. The symbols a, b, and c are parameters that determine the behavior of the function f. For each value of the parameters, we get a different function.
A parameter is a quantity that influences the output or behavior of a mathematical object but is viewed as being held constant. Parameters are closely related to variables, and the difference is sometimes just a matter of perspective. Variables are viewed as changing while parameters typically either don't change or change more slowly. In some contexts, one can imagine performing multiple experiments, where the variables are changing through each experiment, but the parameters are held fixed during each experiment and only change between experiments.
One place parameters appear is within functions. For example, a function might a generic quadratic function as
f(x)=ax2+bx+c.
Here, the variable x is regarded as the input to the function. The symbols a, b, and c are parameters that determine the behavior of the function f. For each value of the parameters, we get a different function.
First week of June!
1st post!
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