High School

Given matrices \( F = [-2, 0, 0, 8, 2, 1] \) and \( C = [12, 0, \frac{3}{2}, 1, -6, 7] \). What is the product \( FC \)?

A. \([-25, 0, -3, 8, -49, 56]\)
B. \([-23, 0, -3, 8, -49, 56]\)
C. \([25, 0, 3, -8, 49, -56]\)
D. \([23, 0, 3, -8, 49, -56]\)

Answer :

Final answer:

To find the product FC of matrices F and C, perform matrix multiplication. The correct option is a. [-25 0 -3 8 -49 56].

Explanation:

In order to find the product FC of matrices F and C, we need to perform matrix multiplication.

Remember that in matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix.

The matrix F has dimensions 2x3 and the matrix C has dimensions 3x2.

Since the number of columns in F is equal to the number of rows in C, we can perform the multiplication.

Multiplying the two matrices, we get FC = [ -25 0 -3 8 -49 56 ].

Therefore, the correct option is a. [-25 0 -3 8 -49 56].

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