document.write( "Question 288488: A is a 2x3 matrix and B a 3x2 matrix is A-B defined\r
\n" ); document.write( "\n" ); document.write( "A is invertible 3x3 matrix B is 3x4 matrix is A to the -1 power B defined\r
\n" ); document.write( "\n" ); document.write( "A is 3x4 matrix and B is 3x4 matrix is A+B defined \r
\n" ); document.write( "\n" ); document.write( "I do not understand what is meant my defined
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Algebra.Com's Answer #209109 by jim_thompson5910(35256) $\"\"$ $\"About$

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In order to add or subtract two matrices, the two matrices need to be of the same size. Since A and B are of different sizes (A is 2x3 but B is 3x2), you CANNOT subtract B from A. It doesn't make sense to subtract the two matrices if they are of different sizes. So A-B is NOT defined.\r
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\n" ); document.write( "\n" ); document.write( "If A is a 3x3 invertible matrix, then $\"A%5E%28-1%29\"$ is also a 3x3 matrix. Because $\"A%5E%28-1%29\"$ has 3 columns and B has 3 rows, this means that the inner dimensions match. This means that you are able to multiply $\"A%5E%28-1%29\"$ and B. So $\"A%5E%28-1%29B\"$ is defined. \r
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\n" ); document.write( "\n" ); document.write( "Since A and B are of the same size, it is perfectly possible to add up the two matrices. So A+B is defined. \n" ); document.write( "

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