Question

Vector space/ vector subspace

Answer 1

ok if u are given a 2x2 matrix .. im curious wat type of question(possible questions ) is likely to come on this topic

Answer 2

the topic is broad, what are you interested to know about a 2x2 matrix

Answer 3

im not sure but but some how i think it will come for my test (anything)

Answer 4

like what are the typical problems your teach talked about in class?

Answer 5

Questions usually comes from problems discussed in so look at lecture notes is a good idea

Answer 6

well this is wat we did so far

Answer 7

@xapproachesinfinity

Answer 8

is that linear algebra?

Answer 9

yep

Answer 10

@amistre64

Answer 11

does that define G as a 2x2 matrix, whose element in 12 is the negative of 21 ?

Answer 12

idk does it?

Answer 13

they are your notes, im just trying to decipher them :)

Answer 14

well yea i think so

Answer 15

would that be an identity or something?

Answer 16

no, it just means if the element in 12 is say: 3, then the element in 21 is: -3

Answer 17

o ok

Answer 18

if we have 2 matrixes; a and b, those elements add to:

(a+b) and (-a-b)

(a+b) and -(a+b) are still opposites after addition

Answer 19

ok i see

Answer 20

so wat type of questions can i expect?

Answer 21

@amistre64

Answer 22

i wouldnt know

Answer 23

for my tests i just walked in and did the work for them ... never bothered with studying or worrying about what might be on it. i either knew it or i didnt :)

Answer 24

ok but if and identity question come do u know of any example

Answer 25

identity question, the identity element is an element of the set that after the operation an another element, returns the same element.

a+0 = a, 0 is the identity element for addition

a*1 = a, 1 is the identity element for multiplication

AI= IA =A, the identity matrix is a matrix whose diagonal is all 1s and the rest are 0s

Answer 26

ok

Answer 27

im not sure what a good identity question would be tho

Answer 28

if u had this how would u find the identity for it \[\left[\begin{matrix}2 & 5 \\ 4 & 1\end{matrix}\right]\]

Answer 29

it is its own identity. you mean inverse?

Answer 30

one way to find an inverse to to row reduce it next to the identity matrix

Answer 31

2 5 1 0 --> 1 0 a b
4 1 0 1 --> 0 1 c d

ab
cd is therefore the inverse sought after

Answer 32

is that a 2x2 matrix

Answer 33

2 5 1 0
4 1 0 1

4 10 2 0
4 1 0 1

2 5 1 0
0 9 2 -1

1 5/2 1/2 0
0 9 2 -1


1 5/2 1/2 0
0 1 2/9 -1/9

1 5/2 1/2 0
0 -5/2 -5/9 5/18

1 0 -1/18 5/18
0 1 4/18 -2/18

Answer 34

its a 2x2 yes, but augmented into a 2x4 might be proper terminology

Answer 35

the other way to find the inverse of a 2x2 is by a memorized process

swap a for d, negate b and c, and divide thru by the determinant

2 5
4 1 det = 2(1)-5(4) = -18,

a=2,d=1, b=5,c=4

-1/18 5/18
4/18 -2/18

which is the same results as the other method

Answer 36

but this is inverse stuff, which im sure you meant to ask instead of identity stuff.

Answer 37

ok thanks