- #1
lina29
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Homework Statement
Consider the following two system of equations:
y[itex]_{1}[/itex]=-2x[itex]_{1}[/itex]-x[itex]_{2}[/itex]+2x[itex]_{3}[/itex]
y[itex]_{2}[/itex]=2x[itex]_{1}[/itex]+2x[itex]_{2}[/itex]-3x[itex]_{3}[/itex]
y[itex]_{3}[/itex]=-2x[itex]_{1}[/itex]-2x[itex]_{2}[/itex]+2x[itex]_{3}[/itex]
and
z[itex]_{1}[/itex]=3y[itex]_{1}[/itex]-4y[itex]_{2}[/itex]-3y[itex]_{3}[/itex]
z[itex]_{1}[/itex]=3y[itex]_{1}[/itex]-y[itex]_{2}[/itex]-4y[itex]_{3}[/itex]
Rewrite these 2 systems as Ax=y and By=z. Use this to get C so that Cx=z.
a) What is the matrix C?
B) Find the RREF matrix D which is row equivalent to the augmented matrix [C|z]
The Attempt at a Solution
My initial thought was that the matrix A would be:
-2 -1 2
2 2 -3
-2 -2 2
and matrix B:
3 -4 -3
3 -1 -4
and that C would be the product of A and B. However, I realized that since the column of A isn't the same as the row of B I couldn't form a product with them. I'm lost on how to find the matrix C. Do I need to invert a matrix in order to find C (the product)?