11product AB of the two matrices
A= 1 2
3 4
And B= 1 2
3 4
To find the product of two matrices, we need to multiply each element from the first matrix with the corresponding element from the second matrix and sum up the results.
Let's start with the first element of the resulting matrix, which is the product of the first row of matrix A (1 2) with the first column of matrix B (1 3):
1*1 + 2*3 = 1 + 6 = 7
Now, let's move on to the second element of the resulting matrix, which is the product of the first row of matrix A (1 2) with the second column of matrix B (2 4):
1*2 + 2*4 = 2 + 8 = 10
Next, we calculate the third element of the resulting matrix, which is the product of the second row of matrix A (3 4) with the first column of matrix B (1 3):
3*1 + 4*3 = 3 + 12 = 15
Finally, we calculate the fourth element of the resulting matrix, which is the product of the second row of matrix A (3 4) with the second column of matrix B (2 4):
3*2 + 4*4 = 6 + 16 = 22
Therefore, the resulting matrix AB is:
7 10
15 22
To find the product AB of the two matrices A and B, we need to multiply each element of the first row of matrix A by each element of the first column of matrix B, and sum the products.
First, let's write out A and B:
A = 1 2
3 4
B = 1 2
3 4
To find the element at the top-left position of the resulting product matrix AB, we multiply the corresponding elements and add them:
(1 * 1) + (2 * 3) = 1 + 6 = 7
The top-left element of AB is 7.
To find the element at the top-right position, we multiply the corresponding elements and add them:
(1 * 2) + (2 * 4) = 2 + 8 = 10
The top-right element of AB is 10.
Next, we move to the second row of A and calculate the corresponding two elements of AB.
To find the element at the bottom-left position, we multiply the corresponding elements and add them:
(3 * 1) + (4 * 3) = 3 + 12 = 15
The bottom-left element of AB is 15.
To find the element at the bottom-right position, we multiply the corresponding elements and add them:
(3 * 2) + (4 * 4) = 6 + 16 = 22
The bottom-right element of AB is 22.
Therefore, the product AB of matrices A and B is:
AB = 7 10
15 22