Posted by Jennifer on Friday, May 2, 2008 at 3:36pm.
I have a problem with the following homework question:
Which product represents the solution to the system: y + 7x=14
x + 4y=1
a.  (1/27) (4/27)
 (7/27) (1/27)
b.  (7/3) (4/3) 
 (1/3) (1/3) 
c.  (7/3) (4/3) 
 (1/3) (1/3) 
d.  (1/27) (4/27) 
 (4/27) (1/27) 
in every answer above, the matrices are multiplied by
1 
14
I'm totally confused about how they got those answers...I came up with this as a solution: 1/27 mult. by
4 1 
1 7  mult. by
14 
1 
i'm not sure what i'm doing wrong...
i really need help with this question. thanks in advance!

mathmatrix equations  Damon, Friday, May 2, 2008 at 5:31pm
7 1 14
1 4 1
divide first row by 7 to get 1 at A11
+1 1/7 + 2
1 + 4 + 1
add them to get 0 in A21
+1 1/7 + 2
+0 27/7 + 3
multiply second row by 7/27 to get 1 in A22
+1 1/7 + 2
+0 + 1 + 7/9
that means y = 7/9. to get rid of the 1/7 in A12, add 1/7 times row 2 to row 1
1 0 19/9
0 1 7/9
so
x = 19/9
y = 7/9
check
y + 7 x = 7/9 +133/9 = 126/9 = 14 check
x+4y = 19/9 + 28/9 = 9/9 = 1 check
I think you may have a typo in the problem statement.

mathmatrix equations  Jennifer, Friday, May 2, 2008 at 5:47pm
no, the problem statement is as it is on my sheet.
do you know how to answer the question how they want it (a, b, c, or d)?

mathmatrix equations  Damon, Friday, May 2, 2008 at 6:25pm
trying inverse at the same time
7 1 14 1 0
1 4 1 0 1
divide first row by 7 to get 1 at A11
+1 1/7 + 2 +1/7 0
1 + 4 + 1 0 1
add them to get 0 in A21
+1 1/7 + 2 1/7 0
+0 27/7 + 3 1/7 1
multiply second row by 7/27 to get 1 in A22
+1 1/7 + 2 1/7 0
+0 + 1 + 7/9 1/27 7/27
that means y = 7/9. to get rid of the 1/7 in A12, add 1/7 times row 2 to row 1
1 0 19/9 4/27 1/27
0 1 7/9 1/27 7/27
That means the inverse is
4/27 1/27
1/27 7/27
that inverse times the column 14 1
should solve it
4/27 1/27  14
1/27 7/27  1
19/9
7/9
caramba

mathmatrix equations  Damon, Friday, May 2, 2008 at 6:28pm
so answer a does it

mathmatrix equations  Damon, Friday, May 2, 2008 at 6:30pm
but I had to multiply by {14 1} not {1 14}

mathmatrix equations  Damon, Friday, May 2, 2008 at 6:33pm
In other words, we agree.

mathmatrix equations  Jennifer, Friday, May 2, 2008 at 7:20pm
thanks, this question is very strange but your replies are veryvery helpful =)
much appreciated!
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