SOLUTION: What are the w, x, y, and z values using this matrix? 1 1 1 1 4 0 1 4 3 8 0 0 1 3/5 9/5 0 0 0 1 -2

Algebra ->  Matrices-and-determiminant -> SOLUTION: What are the w, x, y, and z values using this matrix? 1 1 1 1 4 0 1 4 3 8 0 0 1 3/5 9/5 0 0 0 1 -2      Log On


   

Question 564321: What are the w, x, y, and z values using this matrix?
1 1 1 1 4
0 1 4 3 8
0 0 1 3/5 9/5
0 0 0 1 -2
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!


This matrix is in "row echelon" form because each
row's left-most non-zero element is 1 and they
move to the right as we go down the matrix.  So the
matrix is an abbreviation for this system:


Removing all the 1 coefficients and the 0 terms:


We use "back substitution".

The bottom, fourth, equation is already solved for z,

so we substitute -2 for z in the third equation:

y+%2B+expr%283%2F5%29z+=+9%2F5

y+%2B+expr%283%2F5%29%28-2%29+=+9%2F5

y+-+6%2F5+=+9%2F5

y+=+9%2F5+%2B+6%2F5

y+=+15%2F5

y+=+3

Now we substitute 3 for y and -2 for z in the
second equation:

x++%2B++4y+%2B+++3z+=+8
x++%2B++4%283%29+%2B++3%28-2%29+=+8
x+%2B+12+-+6+=+8
x+%2B+6+=+8
x+=+2


Finally we substitute 2 for x, 3 for y 
and -2 for z in the first equation:

w+++%2Bx++%2B++y+%2B+++z+=+++4
w%2B2+%2B+3+-+2+=+4
w+%2B3+=+4
w=1

Solution (w,x,y,z) = (1,2,3,-2)

Edwin