which matrix represents the system of equations below -12x-13y+13z=15
OH yes woops. Here is the rest of the system.
-12x-13y+13z=15
7x-10y-3z=11
7x+14y+5z==-5
Matrices do not do well here, so take a look here. The matrix of coefficients is shown. The augmented matrix contains the extra column of (15,11,-5) as shown in the solution
http://www.wolframalpha.com/input/?i=%7B%7B-12,-13,13%7D,%7B7,-10,-3%7D,%7B7,14,5%7D%7D*%7B%7Bx%7D,%7By%7D,%7Bz%7D%7D+%3D+%7B%7B15%7D,%7B11%7D,%7B-5%7D%7D
The answers are messy; I'd double-check for typos
I think you left something out, no?
Alright thank you! That was one of the answers. Do you think you could help me with a few more questions?
Well, this system of equations seems to be pretty tired and wants to take a nap. I suggest we call it the "Sleepy System." Now, let's put on our funny hats and create a matrix to represent it:
⎡ -12 -13 13 ⎤
⎣ 0 0 0 ⎦
Remember, my dear friend, a matrix is just a grid to organize numbers. In this case, we have -12, -13, and 13 representing the coefficients of x, y, and z, respectively. Since there are no constants on the right side, we have zeros in the second row. Now, let's get some caffeine to wake up this Sleepy System!
To represent the system of equations using a matrix, we need to rewrite the equation in matrix form.
The system of equations:
-12x - 13y + 13z = 15
In matrix form, we represent the coefficients of the variables and the constant terms in a matrix. Let's call this matrix A.
A = [(-12 -13 13)]
Now, let's define another matrix, let's call it X, which represents the variables x, y, and z.
X = [(x),
(y),
(z)]
Finally, we can represent the system of equations in matrix form as:
A * X = B
where B is a column matrix that represents the constant terms of the equations.
B = [(15)]
Therefore, the matrix representation of the system of equations is:
[(-12 -13 13)] * [(x), = [(15)]
(y),
(z)]