MATRICES AND DETERMINANTSHigher Concepts of MathematicsMultiplicationofaMatrixbyaMatrixTo multiply two matrices, the first matrix must have the same number of rows (m) as the secondmatrix has columns (n). In other words, m of the first matrix must equal n of the second matrix.For example, a 2 x 1 matrix can be multiplied by a 1 x 2 matrix,xya bax bxay byor a 2 x 2 matrix can be multiplied by a 2 x 2. If an m x n matrix is multiplied by an n x pmatrix, then the resulting matrix is an m x p matrix. For example, if a 2 x 1 and a 1 x 2 aremultiplied, the result will be a 2 x 2. If a 2 x 2 and a 2 x 2 are multiplied, the result will be a2 x 2.To multiply two matrices, the following pattern is used:Aa bc dBw xy zCABaw by ax bzcw dy cx dzIn general terms, a matrix C which is a product of two matrices, A and B, will have elementsgiven by the following.cij= ai1b1j+ aj2b2j+ + + . . . + ainbnjwherei = ith rowj = jth columnExample:Multiply the matrices A x B.A1 23 4B3 50 6MA-05 Page 20 Rev. 0
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