Question

Dimensions in 3×3 Matrix times a 1×3 Matrix:
a) 3×1
b) 1×3
c) 3×3
d) 1×1

Answer 1

The multiplication of a 3x3 matrix by a 1x3 matrix is not possible due to the rules of matrix multiplication, which require the number of columns in the first matrix to match the number of rows in the second.

Step-by-step explanation:

The question is asking about the result of multiplying a 3×3 matrix with a 1×3 matrix. When you multiply matrices, the number of rows of the resulting matrix is determined by the number of rows in the first matrix, and the number of columns is determined by the number of columns in the second matrix. In this case, we have a 3×3 matrix (3 rows, 3 columns) and a 1×3 matrix (1 row, 3 columns).

According to the rules of matrix multiplication, we can only multiply matrices if the number of columns in the first matrix is equal to the number of rows in the second matrix. Here, this condition is not met, hence, these two matrices cannot be multiplied. Therefore, none of the options (a), (b), (c), or (d) are correct. If, however, the question intended to inquire about multiplying a 3×3 matrix with a 3×1 matrix, the result would indeed be a 3×1 matrix.