Find the Variables

Problem

[[9/10,3/10],[1/10,7/10]]*[[x],[y]]=[[u],[v]]

Solution

1. Perform matrix multiplication by multiplying the first row of the matrix by the column vector.

9/10*x+3/10*y=u

2. Perform matrix multiplication by multiplying the second row of the matrix by the column vector.

1/10*x+7/10*y=v

3. Express the system of linear equations that defines the variables u and v in terms of x and y

u=(9*x+3*y)/10

v=(x+7*y)/10

Final Answer

[[9/10,3/10],[1/10,7/10]]*[[x],[y]]=[[(9*x+3*y)/10],[(x+7*y)/10]]

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