Find the Variables

Problem

[[a,b],[c,d]]+[[7,8],[−7,−1]]=[[−1,−6],[7,−10]]

Solution

1. Set up matrix addition by adding the corresponding elements of the two matrices on the left side of the equation.

[[a+7,b+8],[c−7,d−1]]=[[−1,−6],[7,−10]]

2. Create equations for each variable by setting the corresponding entries equal to each other.

a+7=−1

b+8=−6

c−7=7

d−1=−10

3. Solve for a by subtracting 7 from both sides.

a=−1−7

a=−8

4. Solve for b by subtracting 8 from both sides.

b=−6−8

b=−14

5. Solve for c by adding 7 to both sides.

c=7+7

c=14

6. Solve for d by adding 1 to both sides.

d=−10+1

d=−9

Final Answer

[[a,b],[c,d]]=[[−8,−14],[14,−9]]

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