4.5 Multiplication of two matrices<br />Name: Lee ShingKuan<br />MuhamadZaid<br />Chien Shin Yee<br />Lim Si Qi<br />
Introduction<br />We can multiply two matrices if the number of columns in the first matric equal the number of rows in the second matric.<br />The product matric ’s demension are: row of first matric x columns of the second matric<br />Two matric can’t be multiply together because the number of column does not equal to the rows.In this case the multiplication of these two matric is not defined.<br />If we multiply a 2x2 matric with a 2x1 matric ,the product matric is 2x1 : (2x3) (3x1)=(2x1)<br />If we multiply a 2x2 matric with a 1x2 matric ,the matric can’t be multiply:(2x2) (1x2)=(2x1)<br />
How to multiply two matrices?<br />·Matrixmultiplication falls into two general categories: Scalar in which a single number is multiplied with every entry of a matrix. <br />·Multiplication of an entire matrix by another entire matrix For the rest of the page, matrix multiplication will refer to this second category. <br />
Example:<br />In the picture on the left, the matrices can be multiplied since the number of columns in the 1st one, matrix A, equals the number of rows in the 2nd, matrix B. <br />The dimensions of the product matrix <br /> - rows of 1st matrix ×columns of 2nd<br /> - 4 × 3<br />
Matrix C and D below cannot be multiplied together because the number of columns in C does not equal the number of rows in D. In this case, the multiplication of these two matrices is not defined.<br />
Matrix multiplication <br /><ul><li>Matrix multiplication is a binary operation that takes a pair of matrices, and produces another matrix.
The process is the same for any size matrix. We multiply across rows of the first matrix and down columns of the second matrix, element by element. We then add the products:
In this case, we multiply a 2 × 2 matrix by a 2 × 2 matrix and we get a 2 × 2 matrix as the result.</li></li></ul><li>Generalized Example<br />If we multiply a 2×3 matrix with a 3×1 matrix, the product matrix is 2×1 <br />Here is how we get M11 and M22 in the product. <br />M11 = r11× t11 + r12× t21 + r13×t31M12 = r21× t11 + r22× t21 + r23×t31<br />