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

2 Answers
Dec 14, 2016

[(4),(-10),(17)]

Explanation:

color(white)(aaa)[A]color(white)(aaaaaaa)[B]color(white)(aaaaa)[C]

[(4,0),(-1,3),(2,-5)] * [(1),(-3)] = [(a), (b),(c)]

color(white)(aa)color(red)3" x "color(blue)2color(white)(aaaa)color(blue)2" x "color(red)1color(white)(aa)color(red)3" x "color(red)1

The size of the first matrix A is "2 x 2" because it has 2 rows and 2 columns. The size of the second matrix B is "2 x 1" because it has 2 rows and 1 column.

When the sizes are written next to each other, the "inner" numbers must match. The "outer" numbers determine the size of the resultant matrix.

The resultant matrix C has been labeled [(a),(b),(c)] and has size 3" x "1.

Position a is in the first row and first column. It's value is obtained by multplying the first row of matrix A by the first column of matrix B.

a=4*1 +0*3=4

Position b is in the second row and first column. It is the result of multiplying the second row of A by the first column of B.

b=-1*1+3*-3=-10

Position c is obtained by multiplying the third row of A by the first column of B.

c=2*1+ -5*-3=17

The answer is then [(4),(-10),(17)]

Dec 14, 2016

Shell wrote a good answer while I was writing mine.