Help with matricies?

Question

my problem looks like this, i tried my best to recreate how it looks so bear with me

..[4 ......y] .. [12 ...-15]
x|.......... .|..=|..............|
..[7 .....2.] ...[21 .......z]

anyway, i know how to do regular ones, but the outside variable (x) is making it more difficult for me to understand...can anyone explain how to do this?

answers to the problem are:

x= 3
y= -5
z= 6

i totally forgot about the rule that each one equals eachother

ex.

x.....y.....z = a.....b.....c

and x=a, y=b, and z=c

thanks for the help guys!

what i was doing was setting up equations to solve by elimination. I was going like:

4x+yx=12-15
7x+2x=21z

Answer 1

When you multiply a matrix by a scalar (a regular number), all you have to do is multiply each element of the matrix by said scalar. Thus,
..[4.......y].....[4x.....yx]
x|...........|..=|.............|
..[7......2.].....[7x ....2x]

So now we know that

..[12...-15].....[4x.....yx]
..|............|..=|.............|
..[21......z].....[7x ....2x]

Thus, 12=4x, so x=3.
yx=-15, so y=-5
z=2x=2*3=6

Cheers!
Nicholas

Answer 2

The x multiplies every term in the first matrix, so it becomes

4x ....... xy

7x ........2x

Then equate each term of the first to each of the second:

First, 4x = 12, then x = 3

Then the lower right corner gives 2x = z so z = 6

finally the upper right corner xy=-15, using x = 5 gives y = -5