Question

Solve this system of equations using the inverse of a matrix:

x + y = 1
2x − z = 5
y − 3z = 6

Hint: AX = B and X = BA-1

x = –2.45, y = 1.73, and z = –1.57

x = 1.73, y = –2.45, and z = –1.57

x = 1.45, y = –2.17, and z = –2.15

x = –2.17, y = 1.45, and z = –2.15

Answer 1

@dan815

Answer 2

@amistre64

Answer 3

oull the coeffs ad row reduce

Answer 4

**pull the coeffs and row reduce

Answer 5

Like 1x and 2x and 1y?

Answer 6

x + y = 1
2x − z = 5
y − 3z = 6

fill in for all variables

1x + 1y + 0z= 1
2x + 0y − 1z = 5
0x + 1y − 3z = 6

now get rid of the variables or keep them, doesnt matter thay are immaterial

row reduce using valid row operations

Answer 7

(1.73)+(-2.45)= doesnt equal 1

Answer 8

what are valid row operations?

Answer 9

scalar multiplication, adding a scaled version of one row to the another .. seems like theres one more basic one that im forgetting

Answer 10

row addition

Answer 11

if you know how to work elimination process, its the same thing ...

Answer 12

@amistre64 I think you're thinking of row interchanging?

Answer 13

1x + 1y + 0z= 1
2x + 0y − 1z = 5
0x + 1y − 3z = 6



1 1 0 1
2 0 -1 5
0 1 -3 6

when we reduce this to the identity matrix on the left, the right column reduces to the solution (a,b,c)

1 0 0 a
0 1 0 b
0 0 1 c

Answer 14

ah yes, swapping rows lol

Answer 15

1 1 0 1
2 0 -1 5
0 1 -3 6

we want a 1 starting row1 and a 0 starting row2, and row3 ...

we have a 1 already, and a 0 down below

lets add a multiple of row1 to row2 such that thats 2 goes to 0; any ideas?

Answer 16

its either this or try to determine an inverse .... this tends to be simpler in my book

Answer 17

so you want a 1 starting row

Answer 18

and a 0 on the second row

Answer 19

for some value k, 1k + 2 = 0 is the thought process we want to occur

Answer 20

wtf

Answer 21

Im thinking about b

Answer 22

if k=-2 we are set for it

so

-2(1 1 0 1)
2 0 -1 5
0 1 -3 6


-2 -2 0 -2 now add first 2 rows to get a new row 2
2 0 -1 5
0 1 -3 6


1 1 0 1
0 -2 -1 3 ; divide by -2 to get a 'leading' 1
0 1 -3 6


1 1 0 1
0 1 -.5 -1.5
0 1 -3 6

col2, wants to be 010 we have 111

add multiples of row2 to row1 and row3 .... that gets us there

Answer 23

ok so multiply row 1 2 3

Answer 24

row 1 is the second one you stated isn't it?

Answer 25

row 1 is the first row. ive already worked it to the reduced form of:

1 1 0 1
0 1 -.5 -1.5
0 1 -3 6

-1 times row2 allows us to eliminate the [1] above it and the [1] below it

Answer 26

1 1 0 1
-1( 0 1 -.5 -1.5)
0 1 -3 6



1 1 0 1
0 -1 .5 1.5
0 1 -3 6

now we can add row2 to row1 and row3 to get us the required 0 entries


1 0 .5 2.5
0 1 -.5 -1.5
0 0 -2.5 7.5


now we work the third row into submission, doing this by hand is of course for the birds lol

Answer 27

mk lol

Answer 28

divide the thrid row by -2.5 to get a leading 1; you see how we are building the left side into:

100
010
001

???

Answer 29

yup

Answer 30

1 0 .5 2.5
0 1 -.5 -1.5
0 0 1 -3

and of course what bites is we get all the way to the end and since none of your options has a -3 for z, it means i cant add or something ..... lets just avoid the errors and do this :)

rref{{1 , 1 , 0 , 1},{2 , 0 , -1 , 5},{0 , 1 , -3 , 6}}

http://www.wolframalpha.com/input/?i=rref%7B%7B1+%2C++1%2C+++0%2C+++++1%7D%2C%7B2%2C+++0%2C++-1%2C++++5%7D%2C%7B0%2C+++1%2C++-3%2C++++6%7D%7D

Answer 31

I didn't think wolfram did matrices

Answer 32

the wolf does just about everything, it getting the syntax correct thats key

Answer 33

ive got to go put my leg up ... the pain is excruciating .. good luck

Answer 34

wait what do I do next

Answer 35

read the last column from the rref; its your solutions

Answer 36

I got z

Answer 37

ut there are 2 zs

Answer 38

so it must be c

Answer 39

1 1 0 1
0 1 -.5 -1.5 <-- i see an error, -1/-2 isnt -1/2
0 1 -3 6



1 1 0 1
0 1 .5 -1.5
0 1 -3 6



1 0 -.5 2.5
0 1 .5 -1.5
0 0 -3.5 7.5


1 0 -.5 2.5
0 1 .5 -1.5
0 0 1 -2.14 <-- thats better, now we are on track

2.14 - 1.5 out y is going to be positive so that leaves us with one option that has to work

Answer 40

2.14(.5) - 1.5

1.07 - 1.5 yeah, its going to be c ...