How do you solve #x + 2y + z = 6#, #2x - y - z = 0#, and #3x + 2y +z = 10# using matrices?
Perform the Gauss Jordan elimination on the augmented matrix
Perform the folowing operations on the rows of the matrix
By signing up, you agree to our Terms of Service and Privacy Policy
#x=2#
#y=0#
#z=4#
Given -
#x+2y+z=6#
#2x-y-z=0#
#3x+2y+z=10#
Answer is developed from the template I created in Excel
By signing up, you agree to our Terms of Service and Privacy Policy
You can solve this system of equations using matrices by representing the coefficients and constants in matrix form and then applying matrix operations to find the values of (x), (y), and (z). First, arrange the coefficients and constants into matrices:
[A = \begin{bmatrix} 1 & 2 & 1 \ 2 & -1 & -1 \ 3 & 2 & 1 \end{bmatrix}]
[X = \begin{bmatrix} x \ y \ z \end{bmatrix}]
[B = \begin{bmatrix} 6 \ 0 \ 10 \end{bmatrix}]
Then, use the matrix equation (AX = B), where (A) is the coefficient matrix, (X) is the column matrix containing the variables, and (B) is the constant matrix. To solve for (X), you can use the formula (X = A^{-1}B), where (A^{-1}) is the inverse of matrix (A).
After finding the inverse of matrix (A), denoted as (A^{-1}), multiply it by matrix (B) to find (X):
[X = A^{-1}B]
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- How do you solve #Ax=B# given #A=((2, 0, 0), (-1, 2, 0), (-2, 4, 1))# and #B=((4), (10), (11))#?
- How do you solve #3^{4x - 4} = 9^{2x + 8}#?
- How do you evaluate #(x^3 + 3x^2 + 16x+48) \div (x+3#)?
- How do you write the partial fraction decomposition of the rational expression #(9x^2+9x+40)/(x(x^2+5))#?
- How do you express #(x^2 - 4) / (x -1)# in partial fractions?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7