Lecture Note

Date: Multiplication of a Matrix by a Matric To mutiply two matrices, the first matrix must have the Same number of rows (m) 95 the second matrix has columns (A) In other words, n of the first matrix must equal n of the second matrix. For example, a 2 x1 matrix can be multiplied by a x 2 mathix, x (a b) ax by y ay by or a 2x2 matrix can be mutiplied by a 2x2. If an mxn matnix is multiplied by an nxp matrix, then the resulting matrix is an mxp matnix. For example, if a 2x1 and a / x2 are multiplied, the result will be a 2x2. If a 2x2 and a 2x2 are multiplied the result will be a 2x2. To mutiply two matrices, the following pattern is one: 9 b w X A- - C of B Y Z C = A. B. = aw + by ax +b2 CW + dy cx + d2 In general terms, a matrix (which is a product of two matrices A and B. will have elements given by the following. Cij = ail b1j + aj2 b2j +++ + 9in 6 nj where: i = ith row J = j th column E xample: Multiply the matrices AXB 1 2 5 A. - B 3 I 0 6 CS Dipindai dengan CamScanner

Date : Solution: (1x3) + (2x0) (1xs) + (2x6) A.B - ( 3x3) t (4x0) (3x5) + (4x6) 3 to 5+12 I to 15 +24 3 17 9 39 If should be noted that the mutiplication of matricess is not usually commutative.

Multiplication of a Matrix by a Matric (Mathematic)

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