document.write( "Question 160683: How do you multiply these matrices?
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Algebra.Com's Answer #118508 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
How do you multiply all of these numbers????
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document.write( "The first matrix has dimensions 4 down by 6 across.\r\n" );
document.write( "That's a 4x6 matrix. \r\n" );
document.write( "The second matrix has dimensions 6 down by 4 across.  \r\n" );
document.write( "That's a 6x4 matrix.\r\n" );
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document.write( "Write    4x6 6x4\r\n" );
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document.write( "The two (blue) inner dimensions are both 6.  They must be the same\r\n" );
document.write( "in order for the matrices to even be multipliable. If they weren't the\r\n" );
document.write( "same, the multiplication would not be defined. Since they are both\r\n" );
document.write( "6, they can be multiplied.  The product matrix will have the two outer\r\n" );
document.write( "(red) dimensions.  They are both 4, so the product matrix will be a \r\n" );
document.write( "4x4 matrix.\r\n" );
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document.write( "Set the product equal to a 4x4 matrix of blanks to\r\n" );
document.write( "fill in.\r\n" );
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document.write( "I won't go through all 16 blanks. I will only tell you how to fill in\r\n" );
document.write( "three of them at random.  Then you will know how to do all the rest.\r\n" );
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document.write( "Let's fill in the blank which is in row 3 and column 2:\r\n" );
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document.write( "Take row 3 from the first matrix:\r\n" );
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document.write( "\"%28matrix%281%2C6%2C0%2C+-1%2C+7%2C+-4%2C+6%2C+-5%29%29\"\r\n" );
document.write( "and column 2 of the second matrix:\r\n" );
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document.write( "\"%28matrix%286%2C1%2C2%2C9%2C-1%2C2%2C+7%2C4%29%29\"\r\n" );
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document.write( "Multiply corresponding elements then add them all:\r\n" );
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document.write( "\"0-9-7-8%2B42-20=-2\"\r\n" );
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document.write( "So put a \"-2\" in the blank in row 3 and column 2:\r\n" );
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document.write( "Next let's fill in the blank in the upper right hand corner.\r\n" );
document.write( "That is the blank in row 1 and in column 4:\r\n" );
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document.write( "Take row 1 from the first matrix:\r\n" );
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document.write( "\"%28matrix%281%2C6%2C7%2C+-6%2C+5%2C+-4%2C+8%2C+1%29%29\"\r\n" );
document.write( "and column 4 from the second matrix:\r\n" );
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document.write( "\"%28matrix%286%2C1%2C4%2C3%2C-9%2C0%2C+-5%2C-1%29%29\"\r\n" );
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document.write( "Multiply corresponding elements then add them all:\r\n" );
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document.write( "\"28-18-45%2B0-40-1=-76\"\r\n" );
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document.write( "So put a \"-76\" in the blank in row 1 and column 4:\r\n" );
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document.write( "One more!\r\n" );
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document.write( "Let's fill in the blank in row 2 and column 1:\r\n" );
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document.write( "Take row 2 from the first matrix:\r\n" );
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document.write( "\"%28matrix%281%2C6%2C-2%2C+1%2C+-8%2C+-3%2C+9%2C+-1%29%29\"\r\n" );
document.write( "and column 1 of the second matrix:\r\n" );
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document.write( "\"%28matrix%286%2C1%2C7%2C8%2C-4%2C3%2C+2%2C-1%29%29\"\r\n" );
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document.write( "Multiply corresponding elements then add them all:\r\n" );
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document.write( "\"-14%2B8%2B32-9%2B18%2B1=36\"\r\n" );
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document.write( "So put a \"36\" in the blank in row 2 and column 1:\r\n" );
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document.write( "Do you see how to do it now?  To fill in any blank in the \r\n" );
document.write( "product matrix, you decide which row and column the blank\r\n" );
document.write( "is in which you want to fill, then get the corresponding \r\n" );
document.write( "row from the first matrix, and the corresponding column \r\n" );
document.write( "from the second matrix, then multiply corresponding elements \r\n" );
document.write( "and add them.  You can fill them in in any order you choose.\r\n" );
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document.write( "When you fill in the rest of the blanks you should have this:\r\n" );
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document.write( "Edwin
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