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Replacement:
Replace a row by adding it to (or subtract from it) a multiple of the other row. For a given row ri, this is written as
ri - srj → ri
Note that when replacing row ri, nothing is multiplied by it. Rather, row rj is multiplied by a scalar s (that could be a fraction) and which is added to or subtracted from row ri.
Matrix solutions to systems of the linear algebraic equations: The linear algebraic equation is an equation of the form a 1 x 1 + a 2 x 2 + a 3 x 3 . . . . a n x n
Cross Product: The cross or outer product a × b of two vectors a and b is defined only whenever both a and b are the vectors in three-dimensional space, that means that they b
Finding sums and products: A very general application of a for loop is to compute sums and products. For illustration, rather than of just printing the integers 1 through 5, w
IS Functions for Strings: There are many functions for strings, that return logical true or false. The function isletter returns the logical true when the character is a lette
Example of Menu driven modular program: As an illustration of such a menu-driven program, we will write a program to discover the constant e. The constant e, known as the n
Illustration of Matrix solutions: For illustration, consider the three equations below with 3unknowns x 1 ,x 2 , and x 3 : We can write this in the form Ax = b here A
Illustration of if - else statement: The one application of an if-else statement is to check for errors in the inputs to a script. For illustration, a former script prompted t
Forward elimination: In forward elimination, we want to obtain a 0 in the a 21 position. To accomplish this, we can alter the second line in the matrix by subtracting from it
Matrix definitions: As we know the matrix can be thought of as a table of values in which there are both rows and columns. The most common form of a matrix A (that is sometime
analyzing traffic; determine motion of flow; calculate tracklets; detect abnormalities;
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