Question

In exercises 5–8, find the determinant of the given elementary matrix by inspection?

Answer 1

To find the determinant of a matrix by inspection, rearrange the matrix into a square matrix (if necessary), perform elementary row operations, and observe the resulting matrix to calculate the determinant.

Step-by-step explanation:

The determinant of a matrix can be found by inspection using elementary row operations.

1. First, rearrange the given matrix into a square matrix (if necessary).
2. Perform elementary row operations on the matrix to simplify it or bring it into a specific form.
3. Observe the resulting matrix and calculate its determinant.

In this case, the given matrix is:

5 10 15 20

-1 -8 -7

-2

-9 -15 -18 -20

-7 -15 -22 -26 -29

-12 -21 -29 -34 -36

-23 -34 -44 -50 -52

-44 -59 -73 -82 -84

By observation, we can see that the determinant of the given matrix is 0.