- #1

- 12

- 0

## Homework Statement

Find the rank of A =

{[1 0 2 0]

[4 0 3 0]

[5 0 -1 0]

[2 -3 1 1]}

## Homework Equations

## The Attempt at a Solution

i row reduced A to be:

{[1 0 0 0]

[0 1 0 -1/3]

[0 0 1 0]}

where do i go from here?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter underacheiver
- Start date

- #1

- 12

- 0

Find the rank of A =

{[1 0 2 0]

[4 0 3 0]

[5 0 -1 0]

[2 -3 1 1]}

i row reduced A to be:

{[1 0 0 0]

[0 1 0 -1/3]

[0 0 1 0]}

where do i go from here?

- #2

Dick

Science Advisor

Homework Helper

- 26,263

- 619

I think you omitted a last row of zeros. Ok, what does rank mean?

- #3

- 12

- 0

Since the column rank and the row rank are always equal, they are simply called the rank of A.

- #4

Dick

Science Advisor

Homework Helper

- 26,263

- 619

Since the column rank and the row rank are always equal, they are simply called the rank of A.

Good! So how many linearly independent rows are there? If you have no idea, quote the definition of linear independence.

- #5

- 12

- 0

so is it 3? because the 2nd and 4th columns are dependent.

- #6

Dick

Science Advisor

Homework Helper

- 26,263

- 619

so is it 3? because the 2nd and 4th columns are dependent.

Yes, the second and fourth columns being dependent means the rank is at most 3. Now you have to check that the three remaining vectors are linearly independent. It's easier to see this if you look at the row reduction.

Share: