Final answer:
To compute AD, multiply matrix A by matrix D. To compute DA, multiply matrix D by matrix A.
AD= [2 2 5; 2 4 15; 2 8 25]
DA= [2 2 2; 2 4 6; 5 10 25]
Step-by-step explanation:
To compute AD and DA with matrices A and D, we perform matrix multiplication. The product of two matrices is calculated by taking the dot product of the rows of the first matrix with the columns of the second matrix. Each element of the resulting matrix is computed one by one.
For AD, we multiply each element of row in A by the corresponding element of column in D and sum those products to find the corresponding element in AD. Similarly, for DA, we multiply each element of row in D by the corresponding element of column in A and sum those products to find the corresponding element in DA.
Since matrix D is a diagonal matrix, the computation simplifies since all off-diagonal entries are zero. The non-zero elements of D will scale the elements of A row-wise for AD and column-wise for DA.
To compute AD, we multiply matrix A by matrix D:
[1 1 1; 1 2 3; 1 4 5] * [2 0 0; 0 2 0; 0 0 5] = [2 2 5; 2 4 15; 2 8 25]
To compute DA, we multiply matrix D by matrix A:
[2 0 0; 0 2 0; 0 0 5] * [1 1 1; 1 2 3; 1 4 5] = [2 2 2; 2 4 6; 5 10 25]