T_

Elimination matrices

An n by n matrix E is called an elimination matrix if it has 1's down the diagonal, and at most one nonzero entry off the diagonal. If the nonzero entry, a, lies in the ith row and jth column, then we write E = E[i,j](a) . So for example,

E = matrix([[1, 0, 0], [-2, 1, 0], [0, 0, 1]]) is the elimination matrix E[2,1](-2)

Consider the matrix A := matrix([[3, 2, 1], [6, 2, 1], [-9, 3, 0]]) . If we multiply the top row of A by -2 and add it to the second row, the 6 turns into a 0, thereby eliminating the first variable from the second equation. This is accomplished by the matrix mulitplication A*E., matrix([[1, 0, 0], [-2, 1, 0], [0, 0, 1]])*matrix([...

SKIP_

QM_[.01;0;0;-1.5]

Starting with the original matrix A above, fill in the elimination matrix E below so that

EA = matrix([[3, 2, 1], [6, 2, 1], [-18, 0, -3/2]])

AH_

E =

AT_[8;3;3;1;0;0;5;1;0;5;3;1]

SKIP_

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A Proposed new answer table format

Ken,

Here is another array format I would like. This one makes use of the fact that Maple exports spreadsheets to tables, and the entries are gifs. For example, look at the following problem (I have changed the names of the tags so that wqs2 will ignore them.

tag aliases

KM_[.01;1.21;1.21;1.33;1.33]

Use the tangent line approximation f(x+h)=f(x)+f '(x)*h to fill in the table of approximate f(x) and f'(x) values for x= .2 and x = .3 shown below.

AP_[8]

x f(x) `f'(x)` = f(x)
0 1 1
.1 1.1 1.1
.2 AT_[6]
.3

0 1
.1 1.1
.2 AT_[6]
.3

RIP_

Note there are 4 answers in the qm line. the AP_[8] tag says to look in the following html table

and replace each empty entry with a textbox 8 chars long. There are 4 empty entries in the table,

matching (in a row by row) fashion the 4 answers given in the qm tag line.

This would be a useful format because the other entries in the table are formatted and presented as gifs.