document.write( "Question 301280: I need help with this problem today. Please help me! I believe that you can multiply the following problem, I just don't know the definition of why: \r
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\n" ); document.write( "\n" ); document.write( "I don't have to multiply them I just have to know wither or not you can and why you can or can't?
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Algebra.Com's Answer #216035 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Sorry, I cannot understand your slashes and commas on the second one.\r\n" );
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document.write( "You should not use slashes or commas when typing matrices \r\n" );
document.write( "just skip spaces between the elements, and line them up,\r\n" );
document.write( "and type ᐸpreᐳ at the beginning of your post and type ᐸ/preᐳ at\r\n" );
document.write( "the end of your post, so the numbers will line up vertically \r\n" );
document.write( "since it will be in what is known as \"courier new font\":\r\n" );
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document.write( "If you meant this:\r\n" );
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document.write( "          [ 3 0] \r\n" );
document.write( "  [2 4 0]×[-2 3] \r\n" );
document.write( "          [ 1 2]\r\n" );
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document.write( "then yes, they can be multiplied.\r\n" );
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document.write( "If you meant this \r\n" );
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document.write( "     [2] [ 3 0] \r\n" );
document.write( "     [4]×[-2 3] \r\n" );
document.write( "     [0] [ 1 2]\r\n" );
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document.write( "then no they cannot.\r\n" );
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document.write( "Rule:  \r\n" );
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document.write( "1.  Find the dimension of the first matrix, by first finding\r\n" );
document.write( "    the \"down\" number counting the number of numbers going \r\n" );
document.write( "    from top to bottom and then counting the \"across\" number \r\n" );
document.write( "    of numbers going from right to left.  The dimension of the \r\n" );
document.write( "    matrix is the \"down\" number by the \"across\" number.\r\n" );
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document.write( "2.  If the \"across\" number of the first matrix equals the \"down\"\r\n" );
document.write( "    number of the second matrix, then the two matrices can be \r\n" );
document.write( "    multiplied, and the product matrix will have the dimensions\r\n" );
document.write( "    of the \"down\" number of the first matrix by the \"across\" number\r\n" );
document.write( "    of the second matrix.\r\n" );
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document.write( "If you meant this:\r\n" );
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document.write( "        [ 3 0] \r\n" );
document.write( "[2 4 0]×[-2 3] \r\n" );
document.write( "        [ 1 2]\r\n" );
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document.write( "Then the first matrix is a \"1 down by 3 across\" matrix and\r\n" );
document.write( "the second one is a \"3 down by 2 across\" matrix.\r\n" );
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document.write( "So yes they can be multiplied because the \"across\" number of the\r\n" );
document.write( "first matrix equals the \"down\" number of the second matrix.  The\r\n" );
document.write( "product matrix will then be a 1 down by 2 across matrix, that is\r\n" );
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document.write( " (1 by 3)×(3 by 2) = (1 by 2)\r\n" );
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document.write( "The two inner dimensions are the same (2), so the product matrix\r\n" );
document.write( "will have the outer two dimensions (1 by 2)\r\n" );
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document.write( "Suppose you have these matrices to multiply:\r\n" );
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document.write( "            [6 3 1 9]\r\n" );
document.write( "[0 5 1 8 7] [4 7 0 3]\r\n" );
document.write( "[7 3 4 2 3]×[2 9 9 5]\r\n" );
document.write( "[7 6 5 6 1] [9 4 2 5]\r\n" );
document.write( "            [8 3 8 7] \r\n" );
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document.write( "This is a \"3 down by 5 across\" times a \"5 down by 4 across\",\r\n" );
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document.write( "so they can be multiplied because\r\n" );
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document.write( " (3 by 5)×(5 by 4) = (3 by 4)\r\n" );
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document.write( "the two inner dimensions are the same (5) and the product\r\n" );
document.write( "matrix will be a 3 by 4 matrix.\r\n" );
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document.write( "However if you reversed them:\r\n" );
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document.write( "[6 3 1 9]\r\n" );
document.write( "[4 7 0 3] [0 5 1 8 7]         \r\n" );
document.write( "[4 7 0 3]×[7 3 4 2 3]\r\n" );
document.write( "[2 9 9 5] [7 6 5 6 1]\r\n" );
document.write( "[9 4 2 5]\r\n" );
document.write( "          \r\n" );
document.write( "then you could not multiply them because \r\n" );
document.write( "this is a \"5 down by 4 across\" times a \"3 down by 5 across\"\r\n" );
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document.write( "and \r\n" );
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document.write( "(5 by 4)×(3 by 5)\r\n" );
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document.write( "cannot be multiplied because the two inner dimenisions 4 and 3\r\n" );
document.write( "are not the same.\r\n" );
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document.write( "If you meant this in the problem you submitted: \r\n" );
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document.write( "     [2] [ 3 0] \r\n" );
document.write( "     [4]×[-2 3] \r\n" );
document.write( "     [0] [ 1 2] \r\n" );
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document.write( "then that would be a \"3 down by 1 across\" times a \"3 down by 2 across\"\r\n" );
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document.write( "(3 by 1)×(3 by 2)\r\n" );
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document.write( "and the inner dimensions are not the same, so they cannot\r\n" );
document.write( "be multiplied.\r\n" );
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document.write( "Hope you understand now.\r\n" );
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document.write( "Edwin

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