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4.6 Cramer’s Rule

4.6 Cramer’s Rule. Using Determinants to solve systems of equations. A system of equations can be written as a matrix. 3x + 5y -2x + 7y becomes the matrix x – 6y + 3z 4y – 8z 5x – 3y becomes I will call this type of matrix an operation matrix.

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4.6 Cramer’s Rule

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  1. 4.6 Cramer’s Rule Using Determinants to solve systems of equations

  2. A system of equations can be written as a matrix 3x + 5y -2x + 7y becomes the matrix x – 6y + 3z 4y – 8z 5x – 3y becomes I will call this type of matrix an operation matrix

  3. Cramer’s Rule using the determinants of two matrices 5x + 4y = 28 Find the determinant of the 3x – 2y = 8 operation matrix

  4. Cramer’s Rule using the determinants of two matrices 5x + 4y = 28 Find the determinant of the 3x – 2y = 8 matrix where one of the variables coefficient are replaced with the answers. When solve for x use Find it determinant We will call this the new answer martix

  5. Cramer’s Rule using the determinants of two matrices Now to solve for x divide the new answer matrix by the operation matrix x is 4; y can be found the same way

  6. Matrix for y New answer matrix Then divide by -22, for the operation matrix

  7. Lets solve this system equations by Cramer’s rule 2x – 3y + z = 5 x + 2y + z = -1 x – 3y + 2z = 1 Need to find the determinants of

  8. Find the determinant We will use this for the denominators in the all the fractions.

  9. Solve for x Replace the x column with the answers. So

  10. Solve for y Replace the y column with the answers. So

  11. Solve for z Replace the z column with the answers. So

  12. Homework Page 192 – 193 # 13,15, 17, 21, 23, 27, 29, 31

  13. Homework Page 192 – 193 # 12, 14, 16, 20, 22, 26, 28, 30

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