I have a matrix with

Question

brackets around
[7 6 ][13]
[14 -6] [8]
and i know there are two separate brackets but on this thing you cant just do one big one..

so if you don't understand the equation that was suppose to go into matricies was
x + y = 13
2x - y = 8
x = 7
y = 6

then i am suppose to figure out these 3 equations to that matrix
-2R1 + R2 >R2
-1/3 R2 > R2
-1R2 + R1 > R1

and my question is for those 3 equations i don't know how to figure them out and they are suppose to be resulting in a matrix with the answers. ?? can some one help me out please

Answer 1

Beats me what you are supposed to do.
Perhaps solve for the inverse as follows:
|+1 +1 | |x| |R1|
|+2 -1 | |y| |R2|
meaning coefficient matrix of numbers times the x,y column equals the R1,R2 column
perform algebra on the rows to get identity matrix on the left so the solution is x, y in terms of R1,R2 (in other words find the inverse matrix)
form matrix augmented
+1 +1 R1
+2 -1 R2
add the two rows to get zero in first row second element
+3 +0 (R1+R2)
+2 -1 R2
divide first row by three to get one in upper left
+1 +0 (R1+R2)/3
+2 -1 R2
subtract twice the first from the second to get zero in lower left
+1 +0 (R1+R2)/3
+0 -1 R2 - (2/3)(R1+R2)
multiply second row by -1 to get 0,1 in second row
+1 +0 (R1+R2)/3
+0 +1 -R2 + (2/3)(R1+R2)

That means that
x = (R1+R2)/3
y = (2/3)(R1+R2) - R2
check that with R1 = 13 and R2 = 8
x = (13+8)/3 = 21/3 = 7 check
y = (2/3)(21) - 8 = 14-8 = 6 check