The power, n, of a matrix, A, is when you multiply the matrix by itself n times. A matrix can only be raised to a power if it has the same number of rows and columns. Below you can visualize how to take the power of a matrix. (Note: The matrix is being multiplied by itself n times)
- Rewrite the problem (expand)
- Multiply the first two matrices
- Multiply the next matrix (if there is one) to the matrix produced in step 2
- Multiply the next matrix (if there is one) to the matrix produced in step 3
And so on until you get your final matrix.
Let’s see some examples of how to take the power of a matrix to better understand..
First example (click here):
1. Rewrite the problem
2. Multiply the first two matrices
1. Rewrite the problem
2. Multiply the first two matrices
3. Multiply the next matrix to the matrix produced in step 2
1. Rewrite the problem
2. Multiply the two matrices
Until next time,
Leah