If A and B are 3×2 matrices, and C is a 7×3 matrix, which of the following are defined? A) C*A B) C^T C) B*C D) A+B E) B^T*C^T F) C−A
A, B, D, and E are defined.
When we multiply matrices, the number of columns of the 1st matrix must equal the number of rows of the 2nd matrix.
When we add or subtract matrices, the number of rows and columns must be the same.
A) If C is 7x3 and A is 3x2, that means C has 3 columns and A has 3 rows. So C * A is defined.
B) When you transpose a matrix, the number of rows and columns are switched. So C^T has 3 rows and 7 columns. So C^T is defined.
C) B has 2 columns and C has 7 rows, so B * C is not defined.
D) Because A and B have the same number of rows and columns, we can add them. So A + B is defined.
E) B^T has 2 rows and 3 columns, and C^T has 3 rows and 7 columns. So B^T has the same number of columns as the number of rows as C^T. So B^T * C^T is defined.
F) C and A have different numbers of rows and columns, so C-A is not defined.