Question

Question #4ca6c

Answer 1

`x = -1/2`
`y = 33`

Explanation:

Let `A = [(4, 1, 3), (5, 2x, -3)]`, `B = [(9, 3),(-6,2),(1,4)]`, `C=[(y,-3),(45,2)]`

Using the properties of matrix multiplication, we know that

`y=c_11`

`= a_11b_11+a_12b_21+a_13b_31`

`=4(9)+1(-6)+3(1)`

`=36-6+3`

`=33`

Similarly, we know that

`2 = c_22`

`=a_21b_12+a_22b_22+a_23b_32`

`=5(3)+2x(2)+(-3)(4)`

`=15+4x-12`

`=4x+3`

`=> 4x = 2-3 = -1`

`=> x = -1/2`

Notice that we didn't need to do all the multiplication. We only needed to multiply rows and columns to get equations containing our variables.

(Also, as a side note, if we did do the full multiplication, we'd find that the book has a mistake, in that `c_12` should be `26`, rather than `-3`)