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Chapter 4: Q 241 (page 458)

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

4-1-2-3-21-2-57

Short Answer

Expert verified

The value of the determinant is-77.

Step by step solution

01

Step 1. Given Information

The given matrix is

4-1-2-3-21-2-57

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 4-1-2

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

=4-21-57-(-1)-31-27-2-3-2-2-5

03

Step 3. Evaluate the determinant

By expanding by minors along the first row we get,

=4-21-57-(-1)-31-27-2-3-2-2-5=4[(-2)(7)-(1)(-5)]+1[(-3)(7)-(-2)(1)]-2[(-3)(-5)-(-2)(-2)]=4[-9]+1[-19]-2[11]=-77

Thus, the determinant is-77.

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