# product matrix

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which product represents the solution to the system 3x+4y=-2 and 2x+5y=6

[3 2]*[-2
[4 5] [6]

1/7[3 2]*[-2]
[4 5] [6]

[5 -2]*[-2]
[-4 3] [6]

1/7[5 -4]*[-2]
[-2 3] [6]

could someone explain

• product matrix -

your given system can be written in the following matrix form
[ 5-4]*[x]=[-2]
[-2 3] [y] [6]

the inverse of the first matrix is
1/17 of
[ 5-4]
[-2 3]

if you multiply the left side by that inverse you get the identity matrix
[1 0]
[0 1]

of course you would then also multiply the right side by that , so it looks like the last answer is the correct one

• product matrix (getting careless) -

oops!!
that first matrix of course should have been

[ 3 4]*[x]=[-2]
[ 2 5] [y] [6]

I copied incorrectly from my paper

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