Matrices?

[thetorsoboy]

Subject. I know how to input data in a matrix, but I don't know what rref(, and that junk means. Help.

[DarkerLine]

det(matrix) - returns the determinant of a square matrix. It's kind of hard to explain what that is if you haven't had the appropriate algebra course. As a matter of fact, if you have had that course, no one tells you what it does and why until several years later when you find out and you're like "So that's why I was learning it!" Anyways, don't worry about it.

matrix^T - it flips the matrix along the diagonal - what used to be rows becomes columns, and what used to be columns becomes rows. Aside from math, what this is mainly useful for is for some of those commands that only work with rows or only with columns.

dim(matrix), {R,C->dim(matrix) - this returns the size of the matrix in {rows, columns} format. You can also change the size of a matrix by storing {rows, columns} to dim(matrixvariable)

Fill(N,matrix) - sets every element in the matrix to N. Remember that the number is the first parameter, not the second as would be more intuitive.

identity(N) - returns a N by N matrix which is all 0s except for the main diagonal which is all 1s. Not much use for it in programming, in mathematics it's useful because any matrix multiplied by the identity matrix is the first matrix itself.

randM(rows, columns) - returns a random matrix with the specified size in rows and columns. The numbers in it range from -9 to 9 as far as I can tell, not very useful I'm afraid.

augment(matrix1,matrix2) - returns a matrix that is matrix1 and matrix2 stuck together sideways. Returns an error if they don't have the same number of rows.

Matr>list(matrix,list1,list2,...) - stores each column of the matrix into the lists you put in. If you put in less lists than there are columns, it will only store the leftmost columns.

list>matr(list1,lis2,...,matrix) - the opposite of that command, combines all the lists together into a matrix with each list as a column.

cumSum(matrix) - applies cumSum( for lists to each column of the matrix.

ref( N by N+1 matrix) - the incomplete form of rref(), see that instead.

rref( N by N+1 matrix) - solves an N-variable system of linear equations put into a matrix. For example, if you have the system
1x+3y=2
1x+2y=1
you convert it to the matrix
[[1,3,2]
.[1,2,1]]
and apply rref( to that matrix. you get
[[1,0,-1]
.[0,1,1]]
which translates back to
1x+0y=-1 (x=-1)
0x+1y=1 (y=1)
and solves the equation for you.

The following are used mainly in solving such equations step by step:

rowSwap(matrix,A,B) - returns a new matrix with row A swapped with row B. Important: it does not change the original matrix.

row+(matrix,A,B) - returns a new matrix with row B added to row A of the old matrix.

*row(A, matrix,B) - returns a new matrix with B added to row A of the old matrix.

*row+(A, matrix,B,C) - returns a new matrix with row B multiplied by A and added to row C.

Don't forget to turn off emoticons! - alexrudd

[thetorsoboy]

Please do that, in explicit detail and email them as well. Thanks. This really helps. (thetorsoboy@gmail.com).

[bukwirm]

These are all listed in the manual as well.

[Weregoose]

DarkerLine explained it here for you, but the second thread
after searching would have given it to you much sooner. ;)

And of course read the manual before asking about syntax!