document.write( "Question 1184453: Suppose A is a 3x2 matrix, B is a pxq and C is a 5x4 matrix. If ABC is defined, then what are p and q? \n" ); document.write( "
Algebra.Com's Answer #815050 by Edwin McCravy(20056)\"\" \"About 
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document.write( "Every matrix has a \"DOWN\" dimension and an \"ACROSS\" dimension. This matrix,\r\n" );
document.write( "for example, where the #'s represent numbers (called \"elements\"):\r\n" );
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document.write( "has a \"DOWN\" dimension of 3, and an \"ACROSS\" dimension of 5. Its dimensions\r\n" );
document.write( "are always taken \"DOWN\" by \"ACROSS\", or 3x5. This matrix:\r\n" );
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document.write( "has a \"DOWN\" dimension of 5, and an \"ACROSS\" dimension of 3. Its dimensions\r\n" );
document.write( "are \"DOWN\" by \"ACROSS\", or 5x3. \r\n" );
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document.write( "In order to multiply a matrix on the left by a matrix on its immediate\r\n" );
document.write( "right, the \"ACROSS\" dimension for the matrix on the left MUST be the same as\r\n" );
document.write( "the \"DOWN\" dimension of the matrix on its immediate right.  Otherwise, their\r\n" );
document.write( "multiplication is not defined.\r\n" );
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document.write( ">>>Suppose A is a 3x2 matrix, B is a pxq and C is a 5x4 matrix. If ABC is\r\n" );
document.write( "defined, then what are p and q?\r\n" );
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document.write( "So \"A\"\"%22%22=%22%22\" and\r\n" );
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document.write( "\"C\"\"%22%22=%22%22\"\r\n" );
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document.write( "with a DOWN dimension of 3 and an ACROSS dimension of 2.\r\n" );
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document.write( "So in order to be able to multiply A on the left by B on its right, the\r\n" );
document.write( "ACROSS number of A must be the same as the DOWN dimension of B, so p, the\r\n" );
document.write( "DOWN dimension of B must be 2.  So p = 2.\r\n" );
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document.write( "Now in order to multiply B on the left by C on its right, the ACROSS\r\n" );
document.write( "dimension of B must equal the DOWN dimension of C, which is 5. So q, the\r\n" );
document.write( "ACROSS dimension of B must equal the DOWN dimension of C, so q=5. \r\n" );
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document.write( "So the dimensions of B must be pxq which are 2x5: \r\n" );
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document.write( "So for ABC to be defined, we must have this sort of thing:\r\n" );
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document.write( "\"ABC\"\"%22%22=%22%22\"\r\n" );
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document.write( "Notice again, that the ACROSS dimension of each matrix on the left must\r\n" );
document.write( "always equal to the DOWN dimension of the matrix next to it on the right.\r\n" );
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document.write( "Edwin
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