Using Determinants to solve systems of equations

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Presentation transcript:

Using Determinants to solve systems of equations 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

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

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

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

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

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

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

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

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

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

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

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