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Chapter 4: Q 240 (page 458)

In the following exercises, evaluate each determinant by expanding by minors along the first row.

-23-1-12-231-3

Short Answer

Expert verified

The value of the determinant is-12.

Step by step solution

01

Step 1. Given Information

The given matrix is

-23-1-12-231-3

We have to evaluate the determinant by expanding by minors along the first row.

02

Step 2. Expand by minors along the first row

The first row is -23-1

Now, let's expand by minors along the first row

=-22-21-3-3-1-23-3-1-1231

03

Step 3. Evaluate the determinant

By expanding by minors along the first row we get,

=-22-21-3-3-1-23-3-1-1231=-2[(2)(-3)-(1)(-2)]-3[(-1)(-3)-(3)(-2)]-1[(-1)(1)-(3)(2)]=-2[-4]-3[9]-1[-7]=8-27+7=-12

Thus, the determinant is-12.

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