Final answer:
Matrix C resulting from the multiplication of A (a 4x8 matrix) and B (an 8x9 matrix) will have dimensions of 4x9. Operations involving cross products and subtractions like A × B or A - B are not defined for matrices A and B. Also, a scalar cannot be equated to a vector as per (g).
Step-by-step explanation:
To determine the size of the matrices resulting from matrix operations involving matrices A, B, and C, we follow the rules of matrix multiplication and addition. The number of rows of the resulting matrix corresponds to the rows of the first matrix, and the number of columns corresponds to the columns of the second matrix. The multiplication of two matrices is only possible if the number of columns in the first matrix is equal to the number of rows in the second matrix.
For the matrix operation C = A · B, this is a standard matrix multiplication operation. Since A is a 4x8 matrix and B an 8x9 matrix, the resulting matrix C will be of size 4x9.
For the operation C = A × B or C = A - B, as in (b), these operations aren't defined for matrices A and B directly because the cross product is only defined for vectors in three-dimensional space, and subtracting B from A is not possible because they are of different sizes.
The matrix operation C = AB, as in (d), once again refers to standard matrix multiplication between A and B, resulting in a 4x9 matrix.
For the operation regarding scalar and vector quantities in (g), this appears to be a confusion between scalar multiplication and matrix operations. In the context of matrix operations, scalars can multiply matrices but cannot be equated to vectors.