Matrix MultiplicationDate: 10/11/2003 at 18:11:26 From: Brooke Subject: multiplying matrices I have been trying to do this problem for a while, but I'm not getting the correct answer. Can you help? [6 4 1] x 2 5 [ -3 0 ] -1 3 I think the result has to have dimensions 1x2, but I don't know how to do the multiplication. Date: 10/24/2003 at 01:19:46 From: Doctor Ian Subject: Re: multiplying matrices Hi Brooke, Let's look at two matrices like | a b | | u v w | | c d | | x y z | | e f | The product of the matrices will look like | a b | | u v w | | ? ? ? | | c d | * | x y z | = | ? ? ? | | e f | | ? ? ? | Each '? will be replaced by the dot product of a row of the first matrix, and a column of the second. For example, | a b | | u v w | | ? ? ? | | c d | * | x y z | = | ? ? ? | | e f | | ? _ ? | ^ | element in 3rd row, 2nd column is dot product of 3rd row of first matrix and 2nd column of second matrix Note that this is _why_ the number of columns in the second matrix has to be the same as the number of rows in the first. What is a dot product? Note that each row of the first matrix has the same number of elements as each column of the second matrix. This isn't an accident. It's a requirement. To find the dot product of the row (e,f) and the column (v,y), we multiply the corresponding elements and add the products: (e,f).(v,y) = ev + fy So this is what goes in the result matrix: | a b | | u v w | | ? ? ? | | c d | * | x y z | = | ? ? ? | | e f | | ? ev+fy ? | Is this enough to get started? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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