#### Study sets matching "linear algebra 2"

#### Study sets matching "linear algebra 2"

linear programming

feasible region

constraint

objective function

process of finding the minimum and maximum value of a functio…

the area of intersection of a system of inequalities

a limit or boundary of a region

the expression that defines the quantity to be maximized or m…

linear programming

process of finding the minimum and maximum value of a functio…

feasible region

the area of intersection of a system of inequalities

Vector Space

If a system is inconsistent, is there…

Span of a vector space (set of vectors…

Linearly dependent

A linear combination of v1...vn with coefficients c1...cn is…

No

The set of all possible linear combinations with vectors in t…

At least one vector in S can be written as a linear combinati…

Vector Space

A linear combination of v1...vn with coefficients c1...cn is…

If a system is inconsistent, is there…

No

Zero Matrix

-A in A+(-A)=0 is called the...

Diagonal Matrix

Identity Matrix

Matrix with all zeros

additive inverse of A

a square matrix whose non-diagonal entries are zeros

a square matrix with ones on the main diagonal and zeros ever…

Zero Matrix

Matrix with all zeros

-A in A+(-A)=0 is called the...

additive inverse of A

Y- intercept

Slope

Slope- intercept Form

Point- slope form

the y-coordinate of a point where a graph crosses the y-axis

the steepness of a line on a graph, equal to its vertical cha…

an equation written in the form y=mx+b is in slope-intercept…

y-y1 = m(x-x1), where m is the slope and (x1,y1) is the point…

Y- intercept

the y-coordinate of a point where a graph crosses the y-axis

Slope

the steepness of a line on a graph, equal to its vertical cha…

Equivalent Matrices have the same...

Column Matrix/Column Vector

Row Matrix/Row Vector

Size of the product of mxn and nxp is

size and entries

Matrix with only one column

Matrix with only one row

mxp

Equivalent Matrices have the same...

size and entries

Column Matrix/Column Vector

Matrix with only one column

Scatter Plot

Correlation

Trend Line

Line of Best Fit

a graph that relates two sets of data by plotting the data as…

relationship between data sets

a line that approximates the relationship between variables o…

a trend line that gives the most accurate model of related data

Scatter Plot

a graph that relates two sets of data by plotting the data as…

Correlation

relationship between data sets

The leading entry of the row is the:

Echelon Matrix Form

Reduced Echelon Matrix Form

Inconsistent/Consistent Matrices and E…

leftmost nonzero entry in that row

1. All nonzero rows are above any rows of zeros... 2. "Stairstep…

1. Same three reqs. as echelon form... 2. Leading entry is 1... 3.…

1. If there is a solution, there is a reduced echelon form to…

The leading entry of the row is the:

leftmost nonzero entry in that row

Echelon Matrix Form

1. All nonzero rows are above any rows of zeros... 2. "Stairstep…

(i,j)-entry of A

The diagonal entries of A

Main diagonal

Diagonal matrix

The entry in A in the ith row and the jth column.

a11, a22,a33...

The diagonal of A formed by the diagonal entries.

A square n x n matrix whose nondiagonal entries are zero.

(i,j)-entry of A

The entry in A in the ith row and the jth column.

The diagonal entries of A

a11, a22,a33...

Definition of a subspace

Column Space

Null Space

Theorem 12 for subspaces

A subspace of R^n is any set H in R^n that has three properti…

The column space of a matrix A is the set Col A of all linear…

The null space of a matrix A is the set Nul A of all solution…

The null space of an mxn matrix A is a subspace of R^n. Equiv…

Definition of a subspace

A subspace of R^n is any set H in R^n that has three properti…

Column Space

The column space of a matrix A is the set Col A of all linear…

system of linear inequalities

solutions of a system

half plane

Optimization

Graph of two linear inequalities using the same variables.

Any ordered pairs (x,y) that makes both inequalities true.

the part of a plane on one side of an indefinitely extended s…

A process in which the minimum or maximum of a quantity is so…

system of linear inequalities

Graph of two linear inequalities using the same variables.

solutions of a system

Any ordered pairs (x,y) that makes both inequalities true.

Linear Equation

System of Linear Equations

Solution of a System

Consistent System

In the variables x1, x2, x3, ...., xn is an equation that can…

A collection of one or more linear equations involving the sa…

a list (s1, s2, ..., sn) of numbers that makes each equation…

A system that has at least one solution

Linear Equation

In the variables x1, x2, x3, ...., xn is an equation that can…

System of Linear Equations

A collection of one or more linear equations involving the sa…

If A is axb and B is cxd, AB has the d…

If two rows of A are interchanged to p…

If one row of A is multiplied by a con…

Found by finding all pivot positions a…

axd (# rows A x # columns B)

detB = - detA

detB = (k)detA

basis for Col(A)

If A is axb and B is cxd, AB has the d…

axd (# rows A x # columns B)

If two rows of A are interchanged to p…

detB = - detA

For an m x n matrix, A, the rank of A…

What is the rank of A^T, the transpose…

True or False: If A is an m x n matrix…

What is the nullity of a 5 x 4 matrix…

The number of leading ones in reduced Echelon form.

The rank of A

True

N(A) = n - R(A) = 4 - 3 = 1

For an m x n matrix, A, the rank of A…

The number of leading ones in reduced Echelon form.

What is the rank of A^T, the transpose…

The rank of A

Diagonal Matrix

Matrix Addition

Addition Properties

When multiplying a matrix by a constant,

square nxn matrix with nonzero diagonal entries and zeros in…

add corresponding entries, matrices must be same size

a) A+B = B+A... b) (A+B)+C = A+(B+C)... c) A+0 = A... d) r(A+B) = rA+r…

all entries are multiplied by the constant

Diagonal Matrix

square nxn matrix with nonzero diagonal entries and zeros in…

Matrix Addition

add corresponding entries, matrices must be same size

standard matrix

onto

one-to-one

zero matrix

For a linear transformation T:R^n->R^m, there exists a unique…

A transformation T:R^n->R^m is onto if every vector b in R^m…

A transformation T:R^n->R^m is one-to-one if every vector b i…

a matrix containing only zeros

standard matrix

For a linear transformation T:R^n->R^m, there exists a unique…

onto

A transformation T:R^n->R^m is onto if every vector b in R^m…

Commutative Property of Addition

Associative Property of Additon

Associative Property of Multiplication

Multiplicative Identity

A + B = B + A

(A + B) + C = A + (B + C)

(cd) A = c (dA)

1(A) = A

Commutative Property of Addition

A + B = B + A

Associative Property of Additon

(A + B) + C = A + (B + C)

Column Space

Null Space

Subspace

Basis for a Subspace

colA is the set of all possible linear combinations of column…

nulA is a set of solutions to Ax=0, Dependent columns

1. 0 vector is in H... 2. If u and v are in H, then u + v is in…

Any set of linearly independent vectors (not unique)

Column Space

colA is the set of all possible linear combinations of column…

Null Space

nulA is a set of solutions to Ax=0, Dependent columns

A Square Matrix that has no inverse.

An n x n matrix A such that if there i…

An m x n matrix A, whose turned into a…

A square n x n matrix whose non diagon…

Singular (Matrix)

Invertible

Transpose

Diagonal Matrix

A Square Matrix that has no inverse.

Singular (Matrix)

An n x n matrix A such that if there i…

Invertible

Similar matrices

Similarity transformation of matrices

Diagonalizable matrix

Diagonalization Theorem.

Matrices A and B such that P^-1AP = B or equivalently A = PBP…

it is when changing A into PDP^-1

A matrix that can be written in factored form as PDP^-1, wher…

An matrix A is diagonalizable if and only if A has n linearly…

Similar matrices

Matrices A and B such that P^-1AP = B or equivalently A = PBP…

Similarity transformation of matrices

it is when changing A into PDP^-1