I have another matirx question. I understand the concepts but am just not seeing it all the way through. This question is killing me!
Question: Solve the system of equations using matrices;
. . ...w +..x +..y +..z =..5
. . ...w + 2x -..y - 2z = -1
. . ...w - 3x - 3y -. .z = -1
. . .2w -. .x + 2y -..z = -2
First I created the matrix:
. . .[ 1..1. .1..1 |..5 ]
. . .[ 1..2 -1 -2 | -1 ]
. . .[ 1 -3 -3 -1 | -1 ]
. . .[ 2 -1..2 -1 | -2 ]
Then I performed the operations:
Row 1 = OK, leave alone.
Row 2 = R2 - R1
Row 3 = R3 - R1
Row 4 = R4 - 2R1
After which I got:
. . .[..1..1..1.. 1 |. .5 ]
. . .[..0..1 -2 -3 |..-6 ]
. . .[..0 -4 -4 -2 |..-6 ]
. . .[..0 -3..0 -3 | -12 ]
Next I did:
Row 1 = OK, leave alone.
Row 2 = OK, leave alone.
Row 3 = R3 + 4R2
Row 4 = R4 + 3R2
To get:
. . .[ 1 1. ..1. ..1 |. ..5 ]
. . .[ 0 1. .-2. .-3 |. .-6 ]
. . .[ 0 0 -12 -14 | -30 ]
. . .[ 0 0. .-6 -12 | -30 ]
Now I'm stuck!!! AM I correct to this point? If so, how do I get -12 to 1? I tried:
Row 3 = R3/-12
Row 4 = 1/2R3 + R4
Which gave me:
. . .[ 1 1..1. ..1 | . .5 ]
. . .[ 0 1 -2. .-3 |..-6 ]
. . .[ 0 0..1 7/6 | 5/2 ]
. . .[ 0 0..0. .-5 | -15 ]
After all the back substition I ended up with:
. . .w = -22/7
. . .x = 31/7
. . .y = 5/7
. . .z = 3
But this doesn't work after I plugged in the original equations to check.
Any help would be GREATLY appreciated.
Thank you!
Question: Solve the system of equations using matrices;
. . ...w +..x +..y +..z =..5
. . ...w + 2x -..y - 2z = -1
. . ...w - 3x - 3y -. .z = -1
. . .2w -. .x + 2y -..z = -2
First I created the matrix:
. . .[ 1..1. .1..1 |..5 ]
. . .[ 1..2 -1 -2 | -1 ]
. . .[ 1 -3 -3 -1 | -1 ]
. . .[ 2 -1..2 -1 | -2 ]
Then I performed the operations:
Row 1 = OK, leave alone.
Row 2 = R2 - R1
Row 3 = R3 - R1
Row 4 = R4 - 2R1
After which I got:
. . .[..1..1..1.. 1 |. .5 ]
. . .[..0..1 -2 -3 |..-6 ]
. . .[..0 -4 -4 -2 |..-6 ]
. . .[..0 -3..0 -3 | -12 ]
Next I did:
Row 1 = OK, leave alone.
Row 2 = OK, leave alone.
Row 3 = R3 + 4R2
Row 4 = R4 + 3R2
To get:
. . .[ 1 1. ..1. ..1 |. ..5 ]
. . .[ 0 1. .-2. .-3 |. .-6 ]
. . .[ 0 0 -12 -14 | -30 ]
. . .[ 0 0. .-6 -12 | -30 ]
Now I'm stuck!!! AM I correct to this point? If so, how do I get -12 to 1? I tried:
Row 3 = R3/-12
Row 4 = 1/2R3 + R4
Which gave me:
. . .[ 1 1..1. ..1 | . .5 ]
. . .[ 0 1 -2. .-3 |..-6 ]
. . .[ 0 0..1 7/6 | 5/2 ]
. . .[ 0 0..0. .-5 | -15 ]
After all the back substition I ended up with:
. . .w = -22/7
. . .x = 31/7
. . .y = 5/7
. . .z = 3
But this doesn't work after I plugged in the original equations to check.
Any help would be GREATLY appreciated.
Thank you!