Final answer:
No, you cannot perform matrix multiplication with mat1 and mat2 because the number of columns in mat1 (8) is not equal to the number of rows in mat2 (8).
Step-by-step explanation:
No, you cannot perform matrix multiplication with mat1 and mat2 because the number of columns in mat1 (8) is not equal to the number of rows in mat2 (8). In order to perform matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix.
you should match the number of columns in the first matrix with the number of rows in the second matrix.
For matrix multiplication to be possible, if the first matrix has dimensions of \( m \times n \) (where \( m \) is the number of rows and \( n \) is the number of columns), then the second matrix must have dimensions of \( n \times p \) (where \( n \) is again the number of rows, which should be the same as the number of columns in the first matrix, and \( p \) is the number of columns).
Only when the inner dimensions match—meaning the columns of the first matrix are equal to the rows of the second matrix—can you multiply the two matrices. In your case: - mat1 is a \( 2 \times 8 \) matrix. It has 2 rows and 8 columns. - mat2 is an \( 8 \times 4 \) matrix. It has 8 rows and 4 columns. Here, the number of columns in mat1 is the same as the number of rows in mat2.
They both have the dimension of 8 in one of their axis. Since these inner dimensions are equal, you can multiply the two matrices.
The result of the matrix multiplication will be a new matrix with the outer dimensions of the factors, meaning the resulting matrix will have the number of rows of the first matrix and the number of columns of the second matrix. Thus, after multiplying mat1 with mat2, you will obtain a matrix with dimensions of \( 2 \times 4 \).