Question

Find the Kronecker products A ⊗B and B ⊗A of A= 1 & 0 3 & 1 quad and B=2 & -1 4 & 2\

Answer 1

To find the Kronecker product of matrices A and B, multiply each element of A with the entire matrix B to create a new matrix. The Kronecker product A ⊗ B is 2, -1, 0, 0, 4, 2, 0, 0. The Kronecker product B ⊗ A is 2, 0, -1, 0, 4, 0, 2, 0.

Step-by-step explanation:

To find the Kronecker product of matrices A and B, we simply multiply each element of A with the entire matrix B to create a new matrix. Here are the steps:

1. Multiply 1 with all the elements of matrix B, which gives us:
   1*2 and 1*(-1)
   1*4 and 1*2
   This results in the first 2x2 submatrix of the Kronecker product.
2. Multiply 0 with all the elements of matrix B, which gives us:
   0*2 and 0*(-1)
   0*4 and 0*2
   This results in the second 2x2 submatrix of the Kronecker product.
3. Combine the submatrices obtained in steps 1 and 2 to obtain the final Kronecker product.

So, the Kronecker product A ⊗ B is:

2 & -1 & 0 & 0

4 & 2 & 0 & 0

To find the Kronecker product B ⊗ A, we follow the same steps but multiply each element of B with matrix A. So the Kronecker product B ⊗ A is:

2 & 0 & -1 & 0

4 & 0 & 2 & 0