Academy Algebra II/Trig

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Do Now: Solve the system of linear equations using matrices (Row Echelon Form)

Academy Algebra II/Trig 12.3: Systems of linear equations: Determinants, 12.4: Inverses Unit 3 Test: Thurs, 10/31 (12.1-12.4, 12.7)

Finding the Determinant for a 2 x 2 Given Then gives you the determinant.

Find the determinant of the matrix. 1.) 2.)

Cramer's Rule Cramer’s Rule can be used to solve a system of equations when the det = 0. Given the system: Using Cramer’s Rule, the solution to the system is given by:

Solve the system using Cramer’s Rule. 1.) 2.)

Finding the Determinant of a 3x3

Evaluate.

Solve the system using Cramer’s Rule.

12.4: Inverse Matrices Two matrices are inverses of each other if their product = identity matrix. The inverse of a 2x2 matrix is Note: Matrix A will not have an inverse if the determinant = 0.

Find the inverse of the matrix, if possible. 1.) 2.)

Finding the Inverse for a 3 x 3 You will find inverses for a 3 x 3 matrix on the calculator. Input the following matrix by creating a new matrix or overwriting a current matrix. Note: Once you are entering #’s in the cells for the matrix you can resize the matrix by selecting the Util menu (F6) – option 6.

Finding the Inverse for a 3 x 3 You will find inverses for a 3 x 3 matrix on the calculator. Input the following matrix by creating a new matrix or overwriting a current matrix. Press Home. Type the name of your matrix and raise it to the -1 exponent. Press ENTER.

Finding the determinant on calculator You can also find determinants for a matrix on the calculator. To find the determinant for this matrix – on your home screen complete the following: Go to MATH menu (Press 2nd 5) Select Matrix, select det( Enter the name of your matrix, close parenthesis. Press ENTER.

Using inverse matrices to solve a linear system. Given system:

Solve the system using Inverses.

Solve the system using Inverses.