Learning matrices right now in math and need help?

Question

x - y + 5z =1
6y - 16z = 28
x + 3y + 2z = 5

Do I just insert a 0 for the missing x? And can you please solve the matrice because i keep trying it and I fail it.

Answer 1

yes, insert 0 for the missing x

So your matrices are this:

1 -1 5 1
0 6 -16 28
1 3 2 5

In your second row, divide by 2 to get:

0 3 -8 14

Subtract this 2nd row from your 3rd row to get the following for your 3rd row:

1 0 10 -9

So your matrices are now as follows:

1 -1 5 1
0 3 -8 14
1 0 10 -9

Keep on manipulating the rows by adding or subtracting till you get to the form of the unit matrix:

1 0 0 A
0 1 0 B
0 0 1 C

at which point your answers will be:

x = A
y = B
z = C

Sorry, can't do ALL your homework for you, but I am more than willing to help. I hope the above helped get you started. Good luck!

Answer 2

If there is a mising therm (like in the 2nd line), you put 0 for it.

Solving a matrix is like solving, in this case, 3 equations with 3 unknowns. You can do all the same tricks in the equation-unknown in the matrix rows.

Each row represents an equation. x1, y1, and z1 are the values of the coefficients of their respective variables. And value is the other side of the equation.

Each row should look like this:
[ x1 y1 z1 | value]

Solving the matrix the equations yield, we can solve for z:

z= -44/23. If you can figure out how, you can solve for x and y as well.

Answer 3

1x-1y+5z=1 -----> [1 -1 5 | 1]
0x+6y-16z=28 --> [0 6 -16 | 28]
1x+3y+2z=5 -----> [1 3 2 | 5]

Now reduce this augmented matrix to row echelon form.

Answer 4

http://calc101.com/webMathematica/matrix-algebra.jsp