SOLUTION: Determine x, y and z for the matrix equation holds: x,y*0,1=6,13 z,4*3,4=12,13

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Question 549623: Determine x, y and z for the matrix equation holds:
x,y*0,1=6,13
z,4*3,4=12,13
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!
The way to multiply two 2×2 matrices is like this:

%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29%28matrix%282%2C2%2Ce%2Cf%2Cg%2Ch%29%29 = %28matrix%282%2C2%2Cae%2Bbg%2Caf%2Bbh%2Cce%2Bdg%2Ccf%2Bdh%29%29

Use that rule to multiply the two 2×2 matrices on the left:

%28matrix%282%2C2%2Cx%2Cy%2Cz%2C4%29%29%28matrix%282%2C2%2C0%2C1%2C3%2C4%29%29 = %28matrix%282%2C2%2C6%2C13%2C12%2C13%29%29

%28matrix%282%2C2%2Cx%2A0%2By%2A3%2Cx%2A1%2By%2A4%2Cz%2A0%2B4%2A3%2Cz%2A1%2B4%2A4%29%29 = %28matrix%282%2C2%2C6%2C13%2C12%2C13%29%29

%28matrix%282%2C2%2C3y%2Cx%2B4y%2C12%2Cz%2B16%29%29 = %28matrix%282%2C2%2C6%2C13%2C12%2C13%29%29

Equate corresponding elements of the matrices on the left
and right:

system%283y=6%2Cx%2B4y=13%2C12=12%2Cz%2B16=13%29

From those you get x=5, y = 2, z = -3

Edwin