How do you multiply $((2, -3), (5, 1))$ by $((1, -3, 4), (2, 4, 3))$ ?

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Answer 1 · 2016-08-18T17:23:00

$((2, -3), (5, 1)) xx ((1, -3, 4), (2, 4, 3)) = ((-4, -18, -1), (7, -11, 23))$

Check that the matrices are compatible.
Look at the format of each matrix - the Rows (R) and the Columns
(C)
R x C

The two 'middle' numbers must be the $color(red)"same"$
$color(blue)(2)xxcolor(red)(2) and color(red)(2)xxcolor(blue)(3)$

These are compatible. The answer will be a $color(blue)(2xx3)$ matrix. $((R_1C_1, R_1C_2, R_1C_3), (R_2C_1, R_2C_2, R_2C_3))$

Each row in matrix 1 must be multiplied by each column in matrix 2.
The elements are all multiplied and then added together.

$((2, -3), (5, 1))$ by $((1, -3, 4), (2, 4, 3)) = ((-4, -18, -1), (7, -11, 23))$

$R_1C_1 = 2-6 = -4$
$R_1C_2 = -6-12 = -18$
$R_1C_3 = 8-9 = -1$
$R_2C_1 = 5+2=7$
$R_2C_2 = -15+4 = -11$
$R_2C_3 = 20+3 = 23$

How do you multiply ((2, -3), (5, 1))((2, -3), (5, 1)) by ((1, -3, 4), (2, 4, 3))((1, -3, 4), (2, 4, 3))?