Question

can a 3x5 coefficient matrix be consistent if it has 3 pivot columns?

Answer 1

3 rows five columns... depends on the situation

Answer 2

okay column 1, 2 and 5

Answer 3

I guess as long as the last two rows are all 0's errrrrrrrrrrrrrr.
you mean that column 1 2 and 5 have leading ones?

Answer 4

what do you have for 3 and 4?

Answer 5

well is there a situation were the matrix is not consistent?

Answer 6

yeah when there are a row of zeros but on the right hand side there is a number

Answer 7

so 0 0 0 0 0 line 3 inconsistent system

Answer 8

many solutions would be 0 0 0 0 0 line 0
consistent also has this ^

Answer 9

ohh yea i now what nonzero row is

Answer 10

but if you have a row that is zero then you cant have 3 pivot columns

Answer 11

well the pivot is a leading one... doesn't it go from the right and to the bottom
1 0 0 0 0 line 2
0 1 0 0 0 line 3
0 0 1 0 0 line 4
0 0 0 1 0 line 5
0 0 0 0 1 line 6

but based on yours
1 0 0 0 0
0 1 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 1

Answer 12

I guess if you switch the rows.. even though it looks kind of whacky, the rules aren't broken. that leading one is going to the bottom and right

Answer 13

1 0 0 0 0
0 1 0 0 0
0 0 0 0 1
0 0 0 0 0
0 0 0 0 0

Answer 14

girl a 3x5 is 0 0 0 0 0
0 0 0 0 0
0 0 0 0 0

Answer 15

oh man thanks... sorry I was multitasking

Answer 16

lol I did a 5 x 5 my bad
1 0 0 0 0
0 1 0 0 0
0 0 0 0 1

Answer 17

there.. looks decent to me.

Answer 18

now lets write it in augmented matrix
1 0 0 0 0 line 3
0 1 0 0 0 line 4
0 0 0 0 1 line 5
looks consistent to me

Answer 19

3equations, 5variables, the rank of the matrix is at most 3, so, if it has 3 pivot columns, it is consistent. why not?