Find the Variables [[6,0],[0,6]][[1,x],[y,1]]=[[6,2],[4,2]]

Problem

[[6,0],[0,6]]*[[1,x],[y,1]]=[[6,2],[4,2]]

Solution

1. Perform matrix multiplication on the left side by multiplying the rows of the first matrix by the columns of the second matrix.

[[6*(1)+0*(y),6*(x)+0*(1)],[0*(1)+6*(y),0*(x)+6*(1)]]=[[6,2],[4,2]]

2. Simplify the resulting matrix on the left side.

[[6,6*x],[6*y,6]]=[[6,2],[4,2]]

3. Equate corresponding entries from the two matrices to create equations for the variables x and y

6*x=2

6*y=4

4. Solve for x by dividing both sides of the first equation by 6.

x=2/6

x=1/3

5. Solve for y by dividing both sides of the second equation by 6.

y=4/6

y=2/3

Final Answer

x=1/3,y=2/3

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