Linear Algebra help please?

qwertykeyboards

ive 2 questions woul be great help if u could help me with them. first one is attached.


2nd one is this:

Show that the two matrices A(its a 2row x 3 column matrix) = (2 -3 -9, 4 -2 2) and B = (1 0 3, 0 1 5) are row equivalent. Find elementary matrices F1,...,Fk such that A = F1,...,FkB. i can do first part of it but dont get the elementary matrices bit.

any help would be appreciated muchly!

Grudaire

qwertykeyboards wrote: »

ive 2 questions woul be great help if u could help me with them. first one is attached.

No it not...

qwertykeyboards wrote: »

Show that the two matrices A(its a 2row x 3 column matrix) = (2 -3 -9, 4 -2 2) and B = (1 0 3, 0 1 5) are row equivalent. Find elementary matrices F1,...,Fk such that A = F1,...,FkB. i can do first part of it but dont get the elementary matrices bit.

To show that they're row equivalent you preform elementary operations on B to get A simply perform these operations on the identity to get what is known as an elementary matrix, so if you interchange the second and third row you can get the same effect by multiplying by:

1 0 0
0 0 1
0 1 0

Try it.

qwertykeyboards

oh yeah you're right it should be attached now!

got the other one done cheers!

Grudaire

Ah, thats simpilly finding a set of linearly independent vectors from the given set, so lets say we have a set S:

s = {x,y,z,w}

then we look at it and we see that

2x + 3y = w and 0x + 0y + 0z = 0 (ie only trival solution to the homogeneous equation)

Then the subset is (basis for subspace)

S' = {x,y,z}