System of Linear Equation and Matrices

Linear Equation

One is the highest exponent

Parametric Representation of a Solution

Infinity many solution

Graphical Method

Substituion Method

Elimination Method

Methods of Linear Equation

slope

y-intercept

y=mx+b where m is the ______ and b is the _______.

Gaussian Elemination

Convert the augmented matrix to Row-Echelon Form (REF).

Gauss-Jordan Elimination

Convert the augmented matrix to Reduced Row-Echelon Form (RREF)

Gaussian + Gauss-Jordan Elimination

transforms the systems augmented matrix using row operations until the solutions become clear.

Row Swapping

Row Scaling

Row Addition

Elementary row operations

Row Swapping

Interchange two rows

Row Scaling

Multiply a row by a non-zero constant.

Row Addition

Add a multiple of one row to another.

Coefficient Matrix

Type of matrix that has coefficient but doesn’t include the constant.

Augmented Matrix

Type of matrix that has coefficient constant.

Matrix

A rectangular array of numbers, symbols, or expressions. Commonly written in box bracket ([])

Row

The horizontal lines of entries and also called as m in a matrix.

Columns

The vertical lines of entries and also called as n in a matrix.

Square matrix

A matrix where m is equal to n or m=n or have the same number of rows and same number of columns.

Diagonal Matrix

The main diagonal should not be same or should not have equal number. The terms off the main diagonal are all zero.

Scalar Matrix

A diagonal matrix whose diagonal elements are equal.

Identity Matrix

A diagonal matrix where all diagonal elements are one (1).

Row Matrix

Matrix where it has only one row.

Column Matrix

Matrix where it has only one columns.

Zero Matrix

Matrix where all elements are zero (0).

Rectangular Matrix

Matrix where number of rows are not equal to the number of columns.

Addition Matrix

The sum A+B of two m-by-n matrices A and B is calculated entry wise (A+B)ij=Aij+Bij.

Undefined

A addition matrix with dont have the same amount or number of element is ______.

Scalar Multiplication

A matrix which every entry of A is being multiplied to c(constant) or (cA)ij=c•Aij.

Matrix Multiplication

If number of columns of the left matrix is the same as the number of rows of the right matrix

Dot Product

If A is an m by n matrix and B is an n by p matrix then their matrix product is m x p matrix whose entries are given by ______ of the corresponding row of A and the corresponding column of B.

n-by-m

What is the transpose of m-by-n is ______.

Matrix Inverse

When multiplied by the original matrix, results in the identity matrix, which is the matrix equivalent of the number '1' in scalar multiplication

Identity Matrix

The matrix B is the inverse of matrix A, if when multiplies together, A*B or B*A gives the _______.

Singular

A matrix that doesn’t have inverse.

Non-Singular

A matrix that have one and only one inverse.

A^-1= 1/ad-bc [d -b -c a]

The inverse (A^-1 )is represented by _______.

Solving System Linear of Equation

If a is invertible matrix, then the system of linear equation Ax=b has unique solutions by x=A^-1b.

x=A^-1b

If a is invertible matrix, then the system of linear equation Ax=b has unique solutions by ______.