This is a homogeneous set of equations.Solve the given linear system by any method
2x1 + x2 + 3x3 = 0
x1 + 2x2 = 0
x2 + x3 = 0
Augmented matrix
2 1 3 0
1 2 0 0
0 1 1 0
Should I begin with a scale operation,
multiply row1 by 1/2 ?
? There's a better way to start, if you would like to get RREF form. Swapping row positions is a valid row operation. Note that moving row1 to the bottom would give us:2 1 3 0
1 2 0 0
0 1 1 0
… multiply row1 by 1/2 ?
Multiply R2 by (-3) and add to R3.R1 <-> R2 first, and then R2 <-> R3
1 2 0 0
0 1 1 0
2 1 3 0
R3 -> -2*R1 + R3
1 2 0 0
0 1 1 0
0 -3 0 0
How can I eliminate the -3 next?
The last row should be [0 0 3 0]Multiply R2 by (3) and add to R3
1 2 0 0
0 1 1 0
0 0 0 0
therefore
x1 + 2x2 = 0
x2 + x3 = 0
I multiplied by 3 instead of -3 otherwise I obtain -6
Bottom row is not correct.…
R3 -> -2*R1 + R3
1 2 0 0
0 1 1 0
0 -3 0 0
Change -3 into 0 by adding 3. There is no other way.How can I eliminate the -3 next?
Subhotosh, frctl made a mistake in the bottom row, earlier (post #5).The last row should be [0 0 3 0]
You tell us!What is this entry supposed to be sorry