Matrices help.?

Question

Solve for K. Thanks for the help!

[h-2 5 ] [-3] = [2h-4]
[4 2+2k ] [4 ] [5k=10]

There are 3 matrices, each have 2 rows. It was a little hard to set up.

Yes you are correct. It should be 5k-10. Thanks

Answer 1

First, compute the bottom row of the product on the left:

(-3)4 + 4(2+2k)

Since the vectors are equal, their components must be equal. So this is equal to the bottom component of the vector on the right, thus:

(-3)4 + 4(2+2k) = 5k+10

Solving:

-12 + 8 + 8k = 5k + 10
3k = 14
k=14/3

And we are done. Note that we didn't have to find the value of h in the process.

Edit: If it's supposed to be 5k-10, the procedure is the same, but we have

(-3)4 + 4(2+2k) = 5k-10
-12 + 8 + 8k = 5k - 10
3k = -6
k = -2

Answer 2

There is a printing error. You have 5k=10. It should be 5k-10?
Multiply the 2 matrices on the left.
(h-2)(-3)+(5)(4) =2h-4 --- (1)
4(-3)+(2+2k)(4)=5k-10 --- (2)
i.e.
solve (1)
-3h+6+20=2h-4
-5h=-30
h=6
solve (2)
-12+8+8k=5k-10
3k=-6
k=-2