Sec. 4-3: Matrix Multiplication 8/24/17

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Sec. 4-3: Matrix Multiplication 8/24/17

Scalar Multiplication: Multiply each element of the matrix by the scalar. (“Scalar” is basically the same as a coefficient.) -3 ½ -6 1 2 = 2 4 4 8

Rules of Matrix Multilplication The number of columns of the 1st matrix must match the number of rows of the 2nd matrix. The resulting product matrix will have the size of the 1st matrix’s ROWS and the 2nd matrix’s COLUMNS. Multiply the ROWS of the 1st matrix by the COLUMNS of the 2nd matrix.

-1 4 3 -2 = 2 -3 7 1 -3 + 28 2 + 4 6 – 21 -4 – 3 = 25 6 -15 -7 Not all matrices can be multiplied together. Also, matrix multiplication is NOT commutative. See board for more examples.

Here are some samples of good & bad matrix multiplication and the resulting product matrix size, if possible. M1x3 x P3x2 = A1x2 A2x4 x B2x4 = not possible S1x3 x T3x4 = P1x4 C7x5 x G7x5 = D2x2 x F2x3 = not possible H2x3

Could these be multiplied? 1 -2 3 4 x -5 2 What would the dimensions be? 1 x 1 [1*4 + (-2)(-5) + 3*2] = [4 + 10 + 6] = [20] Page 182 #1 – 8, 11 – 18