How do you multiply #((1, -3, 2), (2, 1, -3), (4, -3, -1))# and #((2, 1, -1, -2), (3, -2, -1, -1), (2, -5, -1, 0))#?

1 Answer
George C.
Dec 21, 2017

#((1, -3, 2), (2, 1, -3), (4, -3, -1))((2, 1, -1, -2),(3, -2, -1, -1),(2, -5, -1, 0)) = ((-3, -3, 0, 1),(1, 15, 0, -5), (-3, 15, 0, -5))#

Explanation:

For each row of the first matrix and column of the second, sum the products of the three corresponding terms...

#((color(red)(1), color(red)(-3), color(red)(2)), (2, 1, -3), (4, -3, -1))((color(blue)(2), 1, -1, -2),(color(blue)(3), -2, -1, -1),(color(blue)(2), -5, -1, 0)) = ((color(purple)(-3), ?, ?, ?),(?, ?, ?, ?), (?, ?, ?, ?))#

#(color(red)(1))(color(blue)(2))+(color(red)(-3))(color(blue)(3))+(color(red)(2))(color(blue)(2)) = 2-9+4 = color(purple)(-3)#

#((color(red)(1), color(red)(-3), color(red)(2)), (2, 1, -3), (4, -3, -1))((2, color(blue)(1), -1, -2),(3, color(blue)(-2), -1, -1),(2, color(blue)(-5), -1, 0)) = ((-3, color(purple)(-3), ?, ?),(?, ?, ?, ?), (?, ?, ?, ?))#

#(color(red)(1))(color(blue)(1))+(color(red)(-3))(color(blue)(-2))+(color(red)(2))(color(blue)(-5)) = 1+6-10 = color(purple)(-3)#

#dot dot dot#

#((1, -3, 2), (color(red)(2), color(red)(1), color(red)(-3)), (4, -3, -1))((color(blue)(2), 1, -1, -2),(color(blue)(3), -2, -1, -1),(color(blue)(2), -5, -1, 0)) = ((-3, -3, 0, 1),(color(purple)(1), ?, ?, ?), (?, ?, ?, ?))#

#(color(red)(2))(color(blue)(2))+(color(red)(1))(color(blue)(3))+(color(red)(-3))(color(blue)(2)) = 4+3-6 = color(purple)(1)#

#dot dot dot#

#((1, -3, 2), (2, 1, -3), (color(red)(4), color(red)(-3), color(red)(-1)))((2, 1, -1, color(blue)(-2)),(3, -2, -1, color(blue)(-1)),(2, -5, -1, color(blue)(0))) = ((-3, -3, 0, 1),(1, 15, 0, -5), (-3, 15, 0, color(purple)(-5)))#

#(color(red)(4))(color(blue)(-2))+(color(red)(-3))(color(blue)(-1))+(color(red)(-1))(color(blue)(0)) = -8+3+0 = color(purple)(-5)#

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