The prices of the systems are: $1200 for System 1, $1500 for System 2, $1600 for System 3, and $1800 for System 4. Write the information from the table as a 4 x 3 matrix B. Write a row matrix A for which the entries represent the prices for the systems. If C = AB, find c11 . What does this entry of C represent?
To write the information from the table as a 4 x 3 matrix B, we can arrange the prices of the systems in rows and columns as follows:
Matrix B:
| 1200 1500 1600 |
| 1800 |
To write a row matrix A for which the entries represent the prices for the systems, we can list the prices horizontally:
Matrix A:
| 1200 1500 1600 1800 |
Now, let's calculate C = AB. Multiplying matrix A (1 x 4) with matrix B (4 x 3) results in a matrix C (1 x 3).
To find c11, we need to multiply the first row of A with the first column of B and sum the products:
c11 = (1200 * 1200) + (1500 * 1500) + (1600 * 1600) + (1800 * 1800)
Once you calculate this expression, you will find the value for c11. This entry of matrix C represents the sum of the squares of the prices for the systems.