Question

Can someone please help me understand why is this matrix is in REF ?

Answer 1

Weird, I don't think it is because:

Answer 2

But my book says it freakin is tho no cap

Answer 3

Let me cheque again

Answer 4

Maybe I’m loosing touch with sanity... brb

Answer 5

Yup, it says *YES*

Answer 6

hmmmmmm
in this case, I'd ignore the textbook.

Determining whether a matrix is REF or RREF isn't important in linear algebra anyways.
Only turning a matrix into reduced row echelon form is important

Answer 7

But isn’t it already in REF form tho? Or do i need to make some manipulations?

Answer 8

If you divide the first row by 2, it'll become REF

Answer 9

But it wouldn’t make the staircase of *ones* and the formation of triangle underneath the stairs tho

Answer 10

that's okay, it still fits under the definition of:

The first non-zero element in each row, called the leading entry, is 1.
Each leading entry is in a column to the right of the leading entry in the previous row.
Rows with all zero elements, if any, are below rows having a non-zero element.

Answer 11

It still satisfies the definition of REF

Answer 12

What you drew is for a special type of matrix called "invertible matrix", you'll learn about that later.

Answer 13

Wait, what do you mean by.. “ Each leading entry is in a column to the right of the leading entry in the previous row.”??

Answer 14

See how the "leading entry" on the row below is always to the right of the one above?

Answer 15

Yes

Answer 16

that's what it means.

Answer 17

K thanks mate. Really appreciated the effort :)

Answer 18

What do you think @Nnesha ?

Answer 19

I think drawing works fine. It is the typing position that messed up.