DETERMINANTS AND INVERSE MATRICES. I. Determinants of 2x2 A. Formula.

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Presentation transcript:

DETERMINANTS AND INVERSE MATRICES

I. Determinants of 2x2 A. Formula

I. Determinants of 2x2 B. Examples. Find the determinant. Ex 1. Ex 2. Ex 3. Remark: Matrix with determinant 0 is called singular.

II. Determinants of 3x3 A.Steps 1.Rewrite columns 1 and 2 to the right of column 3. 2.Multiply down-diagonals and add them together. 3.Multiply up-diagonals and add them together. 4.Subtract: down-diagonals – up-diagonals

II. Determinants of 3x3 B.Examples. Find the determinant. Ex 1.

II. Determinants of 3x3 B.Examples. Find the determinant. Ex 2.

II. Determinants of 3x3 B.Examples. Find the determinant. Ex 3.

Determine whether A has an inverse. Ex 1. Ex 2.

III. Inverse Matrices A.Formula Given, its inverse is

III.Inverse Matrices B. Examples. Find the inverse of.

III.Inverse Matrices B. Examples. Find the inverse of :

III.Inverse Matrices B. Examples. Find the inverse of.

IV. Solving Matrix Equations Using Inverses AX=B A.Steps 1.Find the inverse of A 2.Multiply A -1 B

IV. Solving Matrix Equations Using Inverses B.Examples. Solve the matrix equation. Ex 1.

IV. Solving Matrix Equations Using Inverses B.Examples. Solve the matrix equation. Ex 2.