Find the Variables [[x+y,y+z],[z+w,w]]=[[3,5],[8,5]]

Problem

[[x+y,y+z],[z+w,w]]=[[3,5],[8,5]]

Solution

1. Equate corresponding elements of the two matrices to create a system of linear equations.

x+y=3

y+z=5

z+w=8

w=5

2. Identify the value of w directly from the fourth equation.

w=5

3. Substitute w=5 into the third equation to solve for z

z+5=8

z=3

4. Substitute z=3 into the second equation to solve for y

y+3=5

y=2

5. Substitute y=2 into the first equation to solve for x

x+2=3

x=1

Final Answer

x=1,y=2,z=3,w=5

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