# Mapping Mathematics_CCOM

## 36 terms · Special topic in Algegra and statistics

đường dây dọi.
(n) đường đo sâu hình quạt
Ship sail along ___ ___ ___ during with radial guiding sounding was conducted from land on Sep. 24 2011.
, One that passes through the center or a circle or arc if executed
, the line that starts at the pivot and extends through the point at which the force is applied

nhân véc tơ

### row reduction

Gaussian elimination
, the process of performing elementary row operations on an augmented matrix to solve a system.

### pivot element

element on the đường chéo () of a matrix

### underdetermined system

system of equations with fewer equations that unknowns; rows < columns (4x8)

### basic variable

Column with 1st non-zero entry in a row is ___ ____.
a variable in a linear system that corresponds to pivot columns in the matrix
, variable in linear system corresponding to a pivot column in coefficient matrix

### free variable

Column with 1st non-zero entry in a row is basic variable, others clumn correspond to ___ ____
any variable in a linear system that does not correspond to a pivot column (creates infinitely many solutions to a consistent matrix)
, A variable in a system of equations for which the other variables can be written in terms of that variable. The variable x3 is a free variable if x1=2x3 and x2=3x3.

### overdetermined system

a system of equations with more equations than unknowns (can be consistent) (8x4)
Ocurrs when the system has been overconstraited - the number of equations outnumbers the number of the unknowns.
, system of equations with more equations that unknowns; rows > columns, Effects of gender often occur simultaneously at multiple levels; interventions often must be multilevel to be successful

### no solution system

This system is called __ ____ system:
1 0 1 : 1/2
0 1 1/4 : 1/4
0 0 0 : 2
vô nghiệm
hen the system of equations have the same slope but different y-intercepts.
, a system of equations in which there are no solutions (the lines are parallel)
, b²-4ac < 0
, no numbers can make the equation true
, An equation that is never true, no matter what value you place in for the variable. Also referred to as "undefined.", when lines have the same slope but different y intercepts in a linear system

### inconsistent system

other way to called a No solution system. ___ ____
parallel lines, no solution, a system of equations that has no solution

### infinite solution

this system is ____ ____ system:
6 0 6 : 2
0 8 2 : 2
0 0 0 : 0
với bất cứ z đều có thể thảo mãn
if the variable is cancelled out and there are 2 numbers that equal each other as the final answer, Planes intersect in a line or planes are all the same plane, If the variable is cancelled out and there are two numbers that equal each other as the final answer, a system of equations in which all values are true (the equations are the same line)

### linear combination

, Given vectors v1, v2,...,vk in Rn and scalars r1, r2,...,rk in Rn, the vector r1v1+r2v2+...+rkvk is the linear combination of the vectors v1, v2,..., vk with scalar coefficients r1,r2,...,rk,

(1) choose one variable to eliminate (2) mutliply one or both equations by factors that make the chosen variable's coefficients opposite numbers (3) add the equations together and solve for the remaining variable (4) take known variable and plug into either equation and solve

### linearly dependent

Some vectors are linearly dependent if Ax = 10 and X <>0(all element).
1 1 2 0 :0
0 -1 0 -2: 0
0 0 1 -3: 0
0 0 0 0 : 0
these are dependent vector because 1z-3w = 0, so with any value of w we can calculate (not measure) z and so forth. so that it satisfies Ax =10 and X <>0.

an indexed set {v1, ..., vp} with the property that the vector equation c1v1 + c2v2 + ... + cnvn = 0 has only the trivial solution
, Pivot in every column (trivial solution), columns of A are linearly independent, Eigenvectors corresponding to distinct eigenvalues are ___________ __________.
, If x₁, x₂,...,xk are mutually orthogonal, they are ______________., an indexed set {v1, ..., vp} with the property that the vector equation c1v1 + c2v2 + ... + cnvn = 0 has only the trivial solution

### one no depending on b

With the Overdetermined system m=n
x x x x g
0 x x x
0 0 x x
0 0 0 x
0 0 0 0
0 0 0 0
When matrix A has full rank: Rank(A) = n. The result is: ______ Solution or __ Solution, ___ ___ _.

### infinite no depending on b

With the Overdetermined system m>n
x x x x
0 x x x
0 0 x x
0 0 0 x
0 0 0 0
0 0 0 0
When matrix A has less than full rank: Rank(A) < n. The result is: ______ Solution or __ Solution, ___ ___ _.
No solution when all the line are in one.

### infinite solution

With the Underdetermined system m<n
x x x x x x
0 x x x x x
0 0 x x x x
When matrix A has full rank :Rank(A) = m. The result is: ______ _____s (any solution is OK)

### infinite solution no depending on b

With the Underdetermined system m<n
x x x x x x
0 x x x x x
0 0 x x x x
When matrix A has less than full rank: Rank(A) < m. The result is: ______ _____s or __ Solution, ___ ___ _.

### one solution

With the square system m=n
x x x
0 x x
0 0 x
When matrix A has than full rank: Rank(A) = m. The result is: ______ _____

### infinite solution no depending on b

With the square system m=n
x x x
0 x x
0 0 x
When matrix A has than full rank: Rank(A) < m. The result is: ______ _____s or ___ solution _______ __ ___

m x n Matrix

### orthogonal

vuông góc (dùng trong toán và khoa học).

### square

Special Matrices:
(m = n) is called: ___ ____ (ma trận vuông).

### diagonal

Special Matrices: ma trận đường chéo.
(m=n, for i=j aij = 0) is called: ____ ___ (đường chéo).
0 x x
x 0 x
x x 0

### scalar

Special Matrices:
(m=n, for i<>j aij = 0, for all i = j, aij = constant is called: _____. ma trận đường chéo hằng số
0 1 0
0 0 1

### identity or unit

Special Matrices: ____ __ ___ matrix
(m=n, for i<>j aij =0, for all i=j aij = 1

### lower triangular

special matrices:
(m = n, aij = 0 for all i<j)
x 0 0
x x 0
x x x

### upper triangular

special matrices:
(m = n, aij = 0 for all i>j)
x x x
0 x x
0 0 x

### symmetric

special matrices: ma trận đối xứng
(m=n, aij = a ji for j<>i)

### Null Matrix

Special Matrices: ma trận 0
(aij = 0 for all i,j)

### nontrivial solution

nghiệm không tầm thường.

### consistent

adj. always being in the same way/
Can an overdetermined linear system (more equations than unknowns) be ____?

### constrait

n. = restriction
_____s of time, money, space.
financial, economic, legal, political constraints.

### rank

n. what is __ of a matrix.
It is:
1. number of base variables
2. -------------- non zero pivot elements
3. --------------- linear independent rows
4. --------------- linear independent columns.

### coincide

v. trùng nhau.
It's a pity our trips to New York don't ____.

### consistent system

system of equations that has at least one solution

### inconsistent system

parallel lines, no solution,
a system of equations or inequalities that has no solution,
A system of equations that has no solutions