Section%206.4%20notes.pdf - Math 0031 Lecture Notes Section...

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Math 0031 Lecture Notes Section 6.4 Section 6.4: Matrix Operations Double Subscript Notation As defined in 6.3, a matrix is a two dimensional array of elements arranged in m rows and n columns (called an m X n matrix). For example, A = 3 5 2 9 7 6 0 1 8 5 4 2 is a 3 X 4 matrix. In order to easily identify elements in a matrix, double subscript notation is used. An element in a matrix is identified generically as: ij a read “a sub i j where i is the row and j is the column of the element. Using double subscript notation in the example above: 2 11 = a 4 12 = a 5 13 = a 8 14 = a 1 21 = a 0 22 = a 6 23 = a 7 24 = a 9 31 = a 2 32 = a 5 33 = a 3 34 = a Addition and Subtraction of Matrices Only matrices of the same dimensions ( m X n ) can be added or subtracted. In order to add or subtract matrices, simply add or subtract the corresponding elements of the two matrices. For example, given two 2 X 2 matrices A and B . A + B = + + + + 22 22 21 21 12 12 11 11 b a b a b a b a A - B = 22 22 21 21 12 12 11 11 b a b a b a b a Similar rules are used for other m X n matrices.
EX: Given the matrices A = 3 9 1 0 7 4 and B = 9 5 6 3 1 8 Determine: A + B = A - B = B - A = Scalar Multiplication When multiplying a matrix by a constant (scalar) factor k , simply multiply every element in the matrix by the scalar factor. Given a 2 X 2 matrix A multiplied by the scalar factor k.

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