How to Find the Product of 2 Matrices
Matrices, the plural form of matrix, are organizational mathematical data sets placed inside brackets. A matrix contains horizontal rows and vertical columns that designate its size. A 2 x 3 matrix, for example, has two rows and three columns. Matrices can be multiplied if the number of columns in the first matrix equals the rows of the second. You can, for example, multiply a 2 x 3 matrix by a 3 x 1 matrix. But you can't multiply a 2 x 5 matrix by a 3 x 1 matrix.
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Instructions
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1
Consider a matrix with two rows and three columns with the top row consisting of "a", "b" and "c" and a bottom row of "d", "e" and "f". Multiply that by a matrix with one column and three rows consisting of "x", "y" and "z".
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Work out the problem, which has a solution matrix of one column and two rows, using this equation for the first solution: (ax) + (by) + (cz). Find the second solution using this equation: (dx) + (ey) + (fz).
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Use the following matrices to work out a numerical example. Fill the matrix with two rows and three columns with the numbers 4, 5 and 2 on the top row and 6, 1 and 10 on the bottom row. Fill the matrix with three rows and one column with the numbers 3, 0 and 7.
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Plug the numbers into the first equation: (ax) + (by) + (cz) = (4 * 3) + (5 * 0) + (2 * 7) = 12 + 0 + 14 = 26. Place "26" into the top row of the solution matrix. Solve the second equation: (dx) + (ey) + (fz) = (6 * 3) + (1 * 0) + (10 * 7) = 18 + 0 + 70 = 88. Place "88" into the bottom row of the solution matrix.
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