A= 4 −2
−1 3
b = 2
1 4

1. is matrix a the inverse of matrix b? show your work, and explain your answer.
2. what is the determinant of matrix b? of matrix a?
leson

1. The matrix A isn't the inverse of matrix B.

2. |B|=12, |A|=12

Step-by-step explanation:

1. We want to know if matrix A is the inverse of matrix B, this means that if you do the product between B and A you have to obtain the identity matrix.

We have:

and

A and B are 2×2 matrices (2 rows and 2 columns), if you multiply them you have to obtain a 2×2 matrix.

Then if A is the inverse of B:

Where,

Observation:

If you have two matrices:

Now:

Then, the matrix A isn't the inverse of matrix B.

2. If you have a matrix A:

The determinant of the matrix is:

Then the determinant of B is:

The determinant of A is:

The one-step transition matrix is:

Step-by-step explanation:

We have 4 states for a the employees:

Of the apprentices (A), 15% are promoted each year to machinists (M) and 15% leave the company (O). Then, 60% of the apprentices stay in the same job.

Of the machinists (M), 10% leave the company (O), so 90% stay as machinists.

Of the master machinists (MM), 5% leave the company (O), so 95% stay as master machinists.

The transition matrix can be written as:

We can calculate the future step from the actual state as: