Question

Use the inverse matrix method to solve:
x+2y -z=10
-2x +3y+z=6
3x-2y+2z=-19
Select one:
a. |1 -3 5|
b. |-1 3 -5|
c. |1 3 5|
d. no solution

Answer 1

If you let \[ \left[ \begin{array}{ccc}
1 & 2 & -1 \\
-2 & 3 & 1 \\
3 & -2 & 2 \end{array} \right]\] be the matrix \(A\), then you can write your system of equations as:

\( \left[ \begin{array}{ccc}
1 & 2 & -1 \\
-2 & 3 & 1 \\
3 & -2 & 2 \end{array} \right]\) \( \left[ \begin{array}{c} x\\y\\z \end{array} \right]\) =\( \left[ \begin{array}{c} 10\\6\\-19 \end{array} \right]\)
or
\(A\vec{x}=\vec{b}\)

So multiplying by the inverse \(A^{-1}\):
\(A^{-1}A\vec{x}=A^{-1}\vec{b}\\
\vec{x}=A^{-1}\vec{b} \)

Now this requires you to invert the matrix \(A\). Can you find the inverse?

Answer 2

is it d?

Answer 3

no

Answer 4

uhhh b?

Answer 5

are you just guessing letters? I just hope you tried attempting it

Answer 6

i am im doing it now

Answer 7

:)

Answer 8

A?

Answer 9

what did you find as the inverse for A?

Answer 10

2

Answer 11

the inverse of a matrix is again a matrix :o

Answer 12

ugg this is hard im really bad at math

Answer 13

maybe this will help..? https://www.khanacademy.org/math/precalculus/precalc-matrices/inverting_matrices/v/inverting-matrices-part-3

Answer 14

explaining how to invert a matrix on here will be very long to type :S

Answer 15

the best i can go with is C?

Answer 16

its looks correct

Answer 17

I don't get C

Answer 18

im going with A

Answer 19

http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi?cmd=inv;m1_1=1;m1_2=2;m1_3=-1;m2_1=-2;m2_2=3;m2_3=1;m3_1=3;m3_2=-2;m3_3=2;curn=3;curn=3;submit21=Submit&hideops=0

Answer 20

I feel like you are just guessing letters :(

Answer 21

im not im just frasturated

Answer 22

The link there shows you all the steps on how to invert a matrix. The last stepis to multiply your inverted matrix with the vector \(\vec{b}\) using matrix multiplication

Answer 23

i got it..........

Answer 24

oh great