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Chapter 4: Q32. (page 186)

Evaluate each determinant using expansion by minors.

376−1628−3−5

Short Answer

Expert verified

The value of the determinant 376−1628−3−5=−265.

Step by step solution

01

- Decide row to use for expansion

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

376−1628−3−5=362−3−5−7−128−5+6−168−3

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.

376−1628−3−5=362−3−5−7−128−5+6−168−3=3−30−−6−75−16+63−48

03

- Multiply and simplify

Further simplify the values.

376−1628−3−5=3−30−−6−75−16+63−48=3−24−7−11+6−45=−72+77−270=−265

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