10_5 - Section 10.5: Matrix Algebra Instructor: Ms. Hoa...

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Section 10.5: Matrix Algebra Instructor: Ms. Hoa Nguyen (nguyen@scs.fsu.edu) 1 Matrix order A matrix with m rows and n columns is said to be an m × n matrix, and of order m × n . 2 Adding and Subtracting Matrices Only matrices with the same order can be added and subtracted. Matrices are added and subtracted term by term, i.e., each entry of one matrix is added or subtracted to the equivalent entry (same row, same column) of the other matrix. Some properties : A + B = B + A A + ( B + C ) = ( A + B ) + C ( k + h ) A = kA + hA k ( A + B ) = kA + kB where A, B, C are matrices with the same rank, and k, h are numbers. 3 Multiplication of Matrices To multiply matrix A with matrix B , the number of columns in A must be the same as the number of rows in B . It means that, matrix multiplication AB is defined if A is a m × n matrix and B is a n × k matrix. The entry at column i and row j of AB is the product of the row i of A and the column j of B . Since the row i of A ( R = ( r
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10_5 - Section 10.5: Matrix Algebra Instructor: Ms. Hoa...

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