High School





12. [-/1 Points) DETAILS LARPCALC10 8.3.053. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use an inverse matrix to solve the system of linear equations, if possible. (If there is no solution, enter NO S

Answer :

Final answer:

To solve a system of linear equations using an inverse matrix, follow these steps:

  1. Represent the system of equations in matrix form.
  2. Create the coefficient matrix A and the constant matrix C.
  3. Find the inverse of the coefficient matrix A.
  4. Multiply the inverse matrix by the constant matrix.
  5. The solution to the system of linear equations is given by the values of x and y in the resulting matrix.

Explanation:

To solve a system of linear equations using an inverse matrix, follow these steps:

  1. Represent the system of equations in matrix form. Let's say we have a system of equations:
  2. a1x + b1y = c1
  3. a2x + b2y = c2
  4. Create the coefficient matrix A and the constant matrix C:
  5. A = [a1 b1; a2 b2]
  6. C = [c1; c2]
  7. Find the inverse of the coefficient matrix A. If the inverse exists, it is denoted as A^(-1):
  8. A^(-1) = 1/(a1b2 - a2b1) * [b2 -b1; -a2 a1]
  9. Multiply the inverse matrix A^(-1) by the constant matrix C:
  10. X = A^(-1) * C
  11. The solution to the system of linear equations is given by the values of x and y in the matrix X:
  12. X = [x; y]

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