Simplify the Matrix

Problem

i*[[−8,9],[6,−9]]−j*[[8,9],[65,−14]]+k*[[−9,5],[−3,−8]]

Solution

1. Calculate the determinant of the first matrix associated with i

|[−8,9],[6,−9]|=(−8)*(−9)−(9)*(6)

72−54=18

2. Calculate the determinant of the second matrix associated with j

|[8,9],[65,−14]|=(8)*(−14)−(9)*(65)

−112−585=−697

3. Calculate the determinant of the third matrix associated with k

|[−9,5],[−3,−8]|=(−9)*(−8)−(5)*(−3)

72−(−15)=87

4. Combine the results using the signs provided in the original expression.

18*i−(−697)*j+87*k

18*i+697*j+87*k

Final Answer

i*[[−8,9],[6,−9]]−j*[[8,9],[65,−14]]+k*[[−9,5],[−3,−8]]=18*i+697*j+87*k

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