Question

Please help
What is the solution of the matrix equation?
[6 5] [x] [2]
[5 4] [y] = [1]

A.(-2, 1)
B.(10, 6)
C.(–4, 3)
D.(–3, 4)

Answer 1

what class is this for?

Answer 2

Alg. 2

Answer 3

so does row reduction mean anything to you? I'm guessing not, but that's ok. There's an easier way.

Answer 4

No, it doesn't I just learned this

Answer 5

just a second I'm double checking my answer so I don't lie to you :)

Answer 6

ok so when we multiply a matrix like this, we start at the top left and multiply whatever is there by the thing on top of the next little matrix. Then we move over and multiply the next number to the right by the second one down in the second matrix. Here's an animation: http://www.facstaff.bucknell.edu/mastascu/elessonsHTML/Circuit/MatVecMultiply.htm

Answer 7

you may have to scroll down just a little to see it.

Answer 8

so the equations we're going to set up is going to look like this: \[6x+5y=2\]and\[5x+4y=1\]

Answer 9

the tricky thing is getting the right numbers paired up together. Remember, go across the row in the first guy and down the column in the second guy.

Answer 10

then you just need to solve those equations for x and y by whatever method you prefer. What answer did you get?

Answer 11

I got c. but I dont think thats right

Answer 12

It's not, but it's awfully close!

Answer 13

If we solve the second eq for x, then \[x=\frac{ 1 }{ 5 }-\frac{ 4 }{ 5}y\]

Answer 14

oh man I picked the hard way. Subbing that in for x in the first one gives\[\frac{ 6 }{ 5}+\frac{ 24 }{ 5 }y+5y=2\]

Answer 15

whoops the 24 should be negative

Answer 16

\[\frac{ 1 }{ 5 }y=\frac{ 4 }{ 5}\]

Answer 17

so y=4

Answer 18

o ok than its d

Answer 19

right. do you understand the pattern?

Answer 20

yes, a little bit

Answer 21

did you watch that animation? That's probably the best way I can explain it over the internet.

Answer 22

yes , I did it was helpful