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If C is a 5x1 matrix and D is a 3x5 matrix, what are the dimensions of DC?

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3 Answers

The formula you want to remember (or write in your notes) is:

( m x n ) x ( n x p ) = ( m x p )

The columns of the first matrix (n) need to equal the rows of the second matrix (n).

In your case, you have:

DC = (3 x 5) x ( 5 x 1)

Applying ( m x n ) x ( n x p ) = ( m x p ), you get the dimensions of DC:

( 3 x 1)

 

Hope that helps!

Remember that matrices have dimensions listed in row,column order so your Matrix C is 5X1 (meaning 5 rows and 1 column) and your Matrix D is 3X5 (meaning 3 rows and 5 columns). When you have an operator between the two matrices, for example D X C, you arrange the dimensions in that same order. In your case, 3X5 x 5x1 and the middle two (columns of the first matrix and rows of the second matrix) MUST match for the operation to be possible. Your resulting matrix will have the rows of the first matrix and the columns of the second, in this case 3x1   Hope this helped!

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