Find AC
A= 2 3 0 C= 2 3
4 1 6 0 1
1 0
Erm....? *I found them!* They're in the 3rd row before the = signs.
Seriously though, I don't get what you're asking...
They didn't line up correctly. I reposted the correct way.
To find the product of matrices A and C, we need to multiply the corresponding elements of the rows of matrix A by the corresponding elements of the columns of matrix C and add the results.
The matrix A has dimensions 2x3 (2 rows, 3 columns), and matrix C has dimensions 3x2 (3 rows, 2 columns). To multiply these matrices, the number of columns in matrix A must be equal to the number of rows in matrix C.
In this case, the number of columns in matrix A (3) matches the number of rows in matrix C (3), so we can proceed with matrix multiplication.
To find the element in the first row, first column (top-left) of the resulting matrix AC, we multiply the corresponding elements of the first row of matrix A with the first column of matrix C and sum them:
AC[0][0] = A[0][0] * C[0][0] + A[0][1] * C[1][0] + A[0][2] * C[2][0]
Substituting the values:
AC[0][0] = 2 * 2 + 3 * 0 + 0 * 1 = 4 + 0 + 0 = 4
Similarly, we can find the other elements of the resulting matrix:
AC[0][1] = A[0][0] * C[0][1] + A[0][1] * C[1][1] + A[0][2] * C[2][1]
= 2 * 3 + 3 * 1 + 0 * 0
= 6 + 3 + 0
= 9
AC[1][0] = A[1][0] * C[0][0] + A[1][1] * C[1][0] + A[1][2] * C[2][0]
= 4 * 2 + 1 * 0 + 6 * 1
= 8 + 0 + 6
= 14
AC[1][1] = A[1][0] * C[0][1] + A[1][1] * C[1][1] + A[1][2] * C[2][1]
= 4 * 3 + 1 * 1 + 6 * 0
= 12 + 1 + 0
= 13
Therefore, the resulting matrix AC is:
AC = 4 9
14 13