document.write( "Question 94381: Find the product:
\n" ); document.write( " $\"%28matrix%283%2C2%2C3%2C-1%2C0%2C4%2C2%2C1%29%29\"$ $\"%28matrix%282%2C3%2C2%2C-1%2C3%2C0%2C-2%2C4%29%29\"$
\n" ); document.write( "`
\n" ); document.write( "Find the product:
\n" ); document.write( " $\"%28matrix%282%2C2%2C3%2C-7%2C1%2C2%29%29\"$ $\"%28matrix%282%2C2%2C0%2C-4%2C5%2C-3%29%29\"$
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #68735 by Edwin McCravy(20081) $\"\"$ $\"About$
You can put this solution on YOUR website!
\r\n" );
document.write( "Find the product:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "An m×n matrix on the left can only be multiplied by an n×p matrix \r\n" );
document.write( "on the right and when they are multiplied the result is an m×p \r\n" );
document.write( "matrix: \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This is a 3×2 matrix times a 2×3 matrix, so m=3, n=2, p=3, so they\r\n" );
document.write( "can be multiplied to give a 3×3 matrix.  Suppose the answer is this\r\n" );
document.write( "3×3 matrix:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "then:\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( " \r\n" );
document.write( "A is in row 1, column 1, so multiply row 1 from \r\n" );
document.write( "the first matrix by column 1 from the second\r\n" );
document.write( "matrix:\r\n" );
document.write( "\r\n" );
document.write( " =  =  = \r\n" );
document.write( "\r\n" );
document.write( "So replace the A by 6.\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( " \r\n" );
document.write( "B is in row 1, column 2, so multiply row 1 from \r\n" );
document.write( "the first matrix by column 2 from the second\r\n" );
document.write( "matrix:\r\n" );
document.write( "\r\n" );
document.write( " =  =  = \r\n" );
document.write( "\r\n" );
document.write( "So replace the B by -1.\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( "C is in row 1, column 3, so multiply row 1 from \r\n" );
document.write( "the first matrix by column 3 from the second\r\n" );
document.write( "matrix:\r\n" );
document.write( "\r\n" );
document.write( " =  =  = \r\n" );
document.write( "\r\n" );
document.write( "So replace the C by 5.\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( "D is in row 2, column 1, so multiply row 2 from \r\n" );
document.write( "the first matrix by column 1 from the second\r\n" );
document.write( "matrix:\r\n" );
document.write( "\r\n" );
document.write( " =  =  = \r\n" );
document.write( "\r\n" );
document.write( "So replace the D by 0.\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( "E is in row 2, column 2, so multiply row 2 from \r\n" );
document.write( "the first matrix by column 2 from the second\r\n" );
document.write( "matrix:\r\n" );
document.write( "\r\n" );
document.write( " =  =  = \r\n" );
document.write( "\r\n" );
document.write( "So replace the E by -8.\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( "F is in row 2, column 3, so multiply row 2 from \r\n" );
document.write( "the first matrix by column 3 from the second\r\n" );
document.write( "matrix:\r\n" );
document.write( "\r\n" );
document.write( " =  =  = \r\n" );
document.write( "\r\n" );
document.write( "So replace the F by 16.\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( "G is in row 3, column 1, so multiply row 3 from \r\n" );
document.write( "the first matrix by column 1 from the second\r\n" );
document.write( "matrix:\r\n" );
document.write( "\r\n" );
document.write( " =  =  = \r\n" );
document.write( "\r\n" );
document.write( "So replace the G by 4.\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( "H is in row 3, column 2, so multiply row 3 from \r\n" );
document.write( "the first matrix by column 2 from the second\r\n" );
document.write( "matrix:\r\n" );
document.write( "\r\n" );
document.write( " =  =  = \r\n" );
document.write( "\r\n" );
document.write( "So replace the H by -4.\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( "I is in row 3, column 3, so multiply row 3 from \r\n" );
document.write( "the first matrix by column 3 from the second\r\n" );
document.write( "matrix:\r\n" );
document.write( "\r\n" );
document.write( " =  =  = \r\n" );
document.write( "\r\n" );
document.write( "So replace the I by 10.\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( "==============================================\r\n" );
document.write( "\r\n" );
document.write( "Find the product: \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This is a 2×2 matrix times a 2×2 matrix, so m=2, n=2, p=2, so they\r\n" );
document.write( "can be multiplied to give a 2×2 matrix.  Suppose the answer is this\r\n" );
document.write( "2×2 matrix:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "then:\r\n" );
document.write( "\r\n" );
document.write( "=\r\n" );
document.write( " \r\n" );
document.write( "A is in row 1, column 1, so multiply row 1 from \r\n" );
document.write( "the first matrix by column 1 from the second\r\n" );
document.write( "matrix:\r\n" );
document.write( "\r\n" );
document.write( " =  = \r\n" );
document.write( "\r\n" );
document.write( "So replace the A by -35.\r\n" );
document.write( "\r\n" );
document.write( "=\r\n" );
document.write( "\r\n" );
document.write( "B is in row 1, column 2, so multiply row 1 from \r\n" );
document.write( "the first matrix by column 2 from the second\r\n" );
document.write( "matrix:\r\n" );
document.write( "\r\n" );
document.write( " =  = =\r\n" );
document.write( "\r\n" );
document.write( "So replace the B by 9.\r\n" );
document.write( "\r\n" );
document.write( "=\r\n" );
document.write( "\r\n" );
document.write( "C is in row 2, column 1, so multiply row 2 from \r\n" );
document.write( "the first matrix by column 1 from the second\r\n" );
document.write( "matrix:\r\n" );
document.write( "\r\n" );
document.write( " =  = =\r\n" );
document.write( "\r\n" );
document.write( "So replace the C by 10.\r\n" );
document.write( "\r\n" );
document.write( "=\r\n" );
document.write( "\r\n" );
document.write( "D is in row 2, column 2, so multiply row 2 from \r\n" );
document.write( "the first matrix by column 2 from the second\r\n" );
document.write( "matrix:\r\n" );
document.write( "\r\n" );
document.write( " =  = =\r\n" );
document.write( "\r\n" );
document.write( "So replace the D by -10.\r\n" );
document.write( "\r\n" );
document.write( "=\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );