Finite Chapter 3.2

# Finite Chapter 3.2 - 4 In general AB ≠ BA Identity Matrix...

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Math 120 SP08 SBrodnick 1 1 3.2 : Matrix Multiplication 2 3.2: Matrix Multiplication * To multiply matrices, “ inner ” two numbers of dimensions must be equal : Can multiply a 3 x 4 matrix and a 4 x 2 matrix: 3 x 4 · 4 x 2 = Can’t multiply a 2 x 3 matrix and a 2 x 4 matrix: 2 x 3 · 2 x 4 3 * To multiply a row matrix A and a column matrix B, multiply each entry in A (from left to right ) by the corresponding entry in B (from top to bottom ), and add the numbers that you get * Calculator error “ Dim Mismatch ” means product not defined 3.2: Matrix Multiplication
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Unformatted text preview: 4 * In general, AB ≠ BA * Identity Matrix ( square matrix) n x n identity matrix I : 1s down main diagonal, 0s everywhere else * Properties of Matrix Multiplication: (P. 191-2) * A(BC) = (AB)C * AI = IA = A * A(B + C) = AB + AC A stays on the left * (A + B)C = AC + BC C stays on the right * (AB) T = B T A T (*order changes) 3.2: Matrix Multiplication 5 * Matrix Form of a System of Linear Equations AX = B Coefficient Matrix Variable Vector Vector of Real Numbers 3.2: Matrix Multiplication...
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