Matrices - Operations MULTIPLICATION OF MATRICES

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Presentation transcript:

Matrices - Operations MULTIPLICATION OF MATRICES The product of two matrices is another matrix To multiply two matrices A and B we must have the number of columns of A must equal the number of rows of B Example. A x B = C (1x3) (3x1) (1x1)

Matrices - Operations B x A = Not possible! (2x1) (4x2) A x B = Not possible! (6x2) (6x3) Example A x B = C (2x3) (3x2) (2x2)

Matrices - Operations Successive multiplication of row i of A with column j of B – row by column multiplication

Matrices - Operations Remember also: IA = A

Matrices - Operations Assuming that the multiplication on the matrices A, B and C are defined, then the following are true: AI = IA = A A(BC) = (AB)C = ABC - (associative law) A(B+C) = AB + AC - (first distributive law) (A+B)C = AC + BC - (second distributive law) Remark: In general, AB not equal to BA, (the matrix BA may not be defined. If AB = 0, neither A nor B necessarily equal to zero. If AB = AC, the matrix B not necessarily equal to C .

Matrices - Operations AB not generally equal to BA, (BA may not be defined)

Matrices - Operations If AB = 0, neither A nor B necessarily equal to zero