Find the Variables

Problem

[[4,−2],[3,0]]+[[w,x],[y,z]]=[[2,−3],[0,5]]

Solution

1. Add the corresponding elements of the two matrices on the left side of the equation to create a single matrix.

[[4+w,−2+x],[3+y,0+z]]=[[2,−3],[0,5]]

2. Set up a system of linear equations by equating the corresponding entries from the left and right matrices.

4+w=2

−2+x=−3

3+y=0

0+z=5

3. Solve for w by subtracting 4 from both sides.

w=2−4

w=−2

4. Solve for x by adding 2 to both sides.

x=−3+2

x=−1

5. Solve for y by subtracting 3 from both sides.

y=0−3

y=−3

6. Solve for z by simplifying the identity.

z=5

Final Answer

w=−2,x=−1,y=−3,z=5

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