# Matrix Operations. Matrix Notation Example Equality of Matrices.

## Presentation on theme: "Matrix Operations. Matrix Notation Example Equality of Matrices."— Presentation transcript:

Matrix Operations

Matrix Notation

Example

Equality of Matrices

Square Matrix

Diagonal Matrix

Triangular Matrices

Row and Column Vectors

Transposition of Vectors

Transposition of Matrices

Example

Symmetric and Skew-Symmetric Matrices

Scalar Multiplication

Zero Matrix

Properties of Scalar Multiplication

Properties of Tranposition

Product of Matricies

Identity Matrices

Identity Property

A System of Linear Equations

The Matrix Equation Ax=b

Properties of Matrix Multiplication

Cautions

Matrix Powers

Theorem

Properties of Transposition

Definition of Linear Combination

Consistency Theorem for Linear Systems A linear system Ax=b is consistent if and only if b can be written as a linear combination of the column vectors of A.

Definition

Matrix Inverse Identities

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