Linear Algebra :D

Linear Systems

100

The amount of solutions for consistent linear system of equations.

what is 1 or more?

200

The elementary operation rules 

1. interchange the order in which the equations are listed

2. multiply any equation by a nonzero number

3. replace any equation with itself added to a multiple of another equation

300

This a system of equations.

what is a list of equations?

400

this considered a system of homogenous equations.

what is when each equation is equal to 0?

500

solve:

6x+y=23

5x-6y=26

(x,y)=(4,-1)

Row Echelon Form

100

The rules of row echelon form

1. All nonzero rows are above any rows of zeros

2. Each leading entry of a row is in a column to the right of the leading entries of any rows above it

3. Each leading entry of a row is equal to 1.

200

The rules of REDUCED row echelon form

1. All nonzero rows are above any rows of zeros

2. Each leading entry of a row is in a column to the right of the leading entries of any rows above

3. Each leading entry of a row is equal to 1.

4. All entries in a column above and below a leading entry are 0.

300

These equations turned into a Augmented Matrix

2x-4y+5z=-2

5x+4y-6z=-4

2x-4y-5z=-6

[2  -4  5  -2]

[5   4 -6  -4]

[2  -4 -5  -6]

400

rank is equal to the number of columns in the matrix.

what happens when the system has one unique solution?

500

inverse matrix rules.

1. square matrix

2. determinant not equal to 0

Determinants

100

Scalar-valued function associated with a square matrix.

what is determinant?

200

LU decomposition equation

L=[1 0] [x 1]

U= [a b] [0 c]

A=[a b] [c d]

300

A=mxn  ?=nxm

what is A^T

400

The equation for A^-1(2x2 matrix)

(1/ad-bc)[d -b][-c a]

500

determinant of 

A=[1 0][-1 -3]

-3

Practice(easy)

100

find the 3 real numbers when

A+B=4

A+C=6

B+C=1

A=4.5

B=-0.5

C=1.5

200

Augmented matrix of

5x-7y+3z=9

4x+10y+6z=-4

2x+6y-13z=-19

[5 -7 3 9]

[4 10 6 -4]

[2 6 -13 -19]

300

compute:

[5 0 1]     _    [2 0 -4]

[4 -3 -5]       [-1 1 -5]

[-7 0 5]

[5 -4 0]

400

is this reduced row echelon form or just row echelon form?

[1 0 3]

[0 1 -5]

[0 0 1]

Row echelon form

500

is the Reduced row echelon form or just row echelon form?

[1 0 0]

[0 3 0]

[0 0 1]

Row echelon form

Practice(hard)

100

Reduce this

[18 20 42]

[-3 -8 -21]

[-3 -4 -9]

[1 0 -1]

[0 1 3]

[0 0 0]

200

find the determinant

[-1 -3 4 -8]

[0 1 -3 3]

[0 0 -2 2]

[0 0 0 3]

A=6

300

Calculate determinant

A=

[4 2 6]

[-2 -1 8]

[0 1 -3]

A=-44

400

Does A= [15 14] [-2 9] have an inverse? How do you know?

yes, the determinant is 163 and it is square.

500

find determinant for the system of equations.

6x+3y+7z=0

-x+y=0

18x+9y+18z=0

A=-27