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Chapter 4: Q31. (page 186)

Evaluate each determinant using expansion by minors.

31.15−4−73263−1

Short Answer

Expert verified

The value of the determinant 15−4−73263−1=172.

Step by step solution

01

- Decide row to use for expansion

In this case, use first row for the expansion by minors.

15−4−73263−1=1323−1−5−726−1+−4−7363

02

- Evaluate 2×2 determinants

The determinant of second order matrix is found by calculating the difference of the product of the two diagonals, that is., abcd=ad−bc. Apply this definition to find the 2×2determinant.

15−4−73263−1=1323−1−5−726−1+−4−7363=−3−6−57−12−4−21−18

03

- Multiply and simplify

Further simplify the values.

15−4−73263−1=−3−6−57−12−4−21−18=−9−5−5−4−39=−9+25+156=172

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