Matrix Multiplication 2x3 times a 3x2

Introduction to Matrix Multiplication Requirements00:00:08

To multiply matrices, specific rules apply. For Matrix A (2x3) and Matrix B (3x2), the number of columns in the first matrix (3) must match the number of rows in the second matrix (3). If these numbers don't align, multiplication isn't possible.

Determining the Resultant Matrix Size00:01:03

The size of the resultant matrix is determined by the outer numbers of the original matrices' dimensions. For a 2x3 matrix multiplied by a 3x2 matrix, the result will be a 2x2 matrix. For example, a 4x5 times a 5x2 would yield a 4x2 matrix.

Calculating the First Row, First Column Element (58)00:01:45

To find the element in the first row, first column of the resulting matrix, multiply the elements of the first row of Matrix A by the elements of the first column of Matrix B and sum them: (1*7) + (2*9) + (3*11) = 7 + 18 + 33 = 58.

Calculating the First Row, Second Column Element (64)00:03:22

For the element in the first row, second column, multiply the first row of Matrix A by the second column of Matrix B: (1*8) + (2*10) + (3*12) = 8 + 20 + 36 = 64.

Calculating the Second Row, First Column Element (139)00:04:28

To find the element in the second row, first column, multiply the second row of Matrix A by the first column of Matrix B: (4*7) + (5*9) + (6*11) = 28 + 45 + 66 = 139.

Calculating the Second Row, Second Column Element (154)00:05:25

Finally, for the element in the second row, second column, multiply the second row of Matrix A by the second column of Matrix B: (4*8) + (5*10) + (6*12) = 32 + 50 + 72 = 154.

Final Resultant Matrix00:06:14

The final 2x2 product matrix is formed by combining these calculated elements: [[58, 64], [139, 154]].