Section 6-2: Matrix Multiplication, Inverses and Determinants There are three basic matrix operations. 1.Matrix Addition 2.Scalar Multiplication 3.Matrix.

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Presentation transcript:

Section 6-2: Matrix Multiplication, Inverses and Determinants There are three basic matrix operations. 1.Matrix Addition 2.Scalar Multiplication 3.Matrix Multiplication

Section 6-2: Matrix Multiplication, Inverses and Determinants Matrix Addition

Section 6-2: Matrix Multiplication, Inverses and Determinants Scalar Multiplication

Section 6-2: Matrix Multiplication, Inverses and Determinants Matrix Multiplication ◦ Not quite as obvious ◦ No counterpart/equivalent operation in the real number system

Section 6-2: Matrix Multiplication, Inverses and Determinants

Example:

Section 6-2: Matrix Multiplication, Inverses and Determinants Example:

Section 6-2: Matrix Multiplication, Inverses and Determinants

Remember that a multiplicative identity for real numbers is 1 because for any real number, a, 1 · a = a. The multiplicative identity n x n square matrix (square means number of rows equals number of columns), is called an identity matrix.

Section 6-2: Matrix Multiplication, Inverses and Determinants

You can write a system of equations as a system of matrices.

Section 6-2: Matrix Multiplication, Inverses and Determinants Example:

Section 6-2: Matrix Multiplication, Inverses and Determinants The multiplicative inverse of a square matrix is called an inverse matrix.

Section 6-2: Matrix Multiplication, Inverses and Determinants Example:

Section 6-2: Matrix Multiplication, Inverses and Determinants If matrix A has an inverse, it is said to be invertible, or nonsingular. A singular matrix does not have an inverse.

Section 6-2: Matrix Multiplication, Inverses and Determinants Example:

Section 6-2: Matrix Multiplication, Inverses and Determinants

Finding the determinant can be helpful in determining whether a matrix has an inverse.

Section 6-2: Matrix Multiplication, Inverses and Determinants Finding the determinant can be helpful in determining whether a matrix has an inverse.

Section 6-2: Matrix Multiplication, Inverses and Determinants Example:

Section 6-2: Matrix Multiplication, Inverses and Determinants

Example:

Section 6-2: Matrix Multiplication, Inverses and Determinants Example:

Section 6-2: Matrix Multiplication, Inverses and Determinants Homework: ◦ Page ◦ #3, 6, 21, 23, 27, 30, 35, 39 ◦ To turn in: #20, 38  Show all work -- only use your calculator to check your work.