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Reduced Row Echelon Form:
The Gauss Jordan technique results in a diagonal form; for illustration, for a 3 × 3 system:
The Reduced Row Echelon Forms take this one step further to answer in all 1's instead of a', therefore the column of b's is the solution:
The MATLAB has a built-in function to do this, known rref. For illustration, for the preceding illustration:
>> a = [1 3 0; 2 1 3; 4 2 3];
>> b = [1 6 3]';
>> ab = [a b];
>> rref(ab)
ans =
1 0 0 -2
0 1 0 1
0 0 1 3
The answer is found from the last column, therefore x1 = -2, x2 = 1, and x3 = 3. To obtain this in a column vector in a MATLAB:
>> x = ans(:,end)
x =
-2
1
3
Displaying expressions: The good-looking function will show such expressions by using exponents; for illustration, >> b = sym('x^2') b = x^2 >> pretty(b)
Execute a exponential function program: Running the script will take up the menu as shown in the figure: Then, what happens will totally depend on which button(s) the
Built-in colormaps: The MATLAB has numerous built-in colormaps which are named; the reference page on colormap shows them. Calling the function colormap without passing any ar
Illustration of Sorting strings: To sort on the rows rather than second dimension should be specified. >> sort(words,2) ans = Hello Hdowy Hi Gbdeo
Illustration of symbolic variable: When, on the other hand, z is a symbolic variable to start with, quotes are not required around the expression, and the words are automatica
Image Processing: The Images are represented as grids, or matrices, of picture elements (known as pixels). In MATLAB an image usually is represented as a matrix in which each
Sound Files: The sound signal is an illustration of a continuous signal which is sampled to result in a discrete signal. In this situation, sound waves traveling through the a
7.13
Gauss Elimination: The Gauss elimination technique consists of: Generating the augmented matrix [A b] Applying EROs to augmented matrix to obtain an upper trian
Uses of Function handles: The Function handles can also be generated for functions other than anonymous functions, both built-in & user-defined functions. For illustration, th
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