Question

Write the augmented matrix for the linear system that corresponds to the matrix equation Ax=b. Then solve the system and write the solution as a vector.
[ 1 2 -1] [ 1]
A=[-3 -4 2], b=[ 2]
[ 5 2 3] [-3]

Answer 1

Ax=b augmented matrix is
[ 1 2 -1 1]
[-3 -4 2 2]
[ 5 2 3 -3]
now you can solve for x,y,z using matrices

Answer 2

can you do it from here?

Answer 3

im trying but i get stuck about half way

Answer 4

ok hold on a min

Answer 5

ok

Answer 6

try to do this
R2= 3R1+R2
R3=-5R1+R3

Answer 7

you get
[ 1 2 -1 1] [ 1 2 -1 1] [ 1 2 -1 1]
[-3 -4 2 2] -->[ 0 2 -1 5] R2/2 -->[ 0 1 -1/2 5/2]
[ 5 2 3 -3] [ 0 -8 8 -8] R3/8 -->[ 0 -1 1 -1] R2+R3 -->

[ 1 2 -1 1] [ 1 2 -1 1]
[ 0 1 -1/2 5/2] [ 0 1 -1/2 5/2]
[ 0 0 1/2 3/2] 2R3--> [ 0 0 1 5]

Answer 8

any question?

Answer 9

see i always get confused on what constant i should multiply each row by to reduce it properly

Answer 10

i did it and got 4, 4, 3 but im pretty sure im wrong

Answer 11

hold on let me re check everything my be i missed something

Answer 12

no i dont think so

Answer 13

im pretty sure im wrong

Answer 14

oooops z=3

Answer 15

[ 1 2 -1 1] [ 1 2 -1 1]
[ 0 1 -1/2 5/2] [ 0 1 -1/2 5/2]
[ 0 0 1/2 3/2] 2R3 [ 0 0 1 3]

Answer 16

yeah i got x=-4, y=4 z=3

Answer 17

oh ok...so i got that answer by multiplying each row by different constants

Answer 18

so thats correct now

Answer 19

does that mean there are different ways to solve the system?

Answer 20

yes, there are other ways to solve the system

Answer 21

ok because i was thinking there was only one certain way to get to the solution

Answer 22

theres Gaussian,etc to name other mathematicians back then

Answer 23

gauss jordan method etc

Answer 24

alright thanks!

Answer 25

ok yw

Answer 26

good luck now