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## Homework Statement

My question involves finding the determinant of a 4x4 matrix, which I know how to do.

The matrix is

0 1 2 3

0 1 2 5

0 3 5 6

0 0 0 0

Since the matrix has zeros in every row and column, its determinant will equal 0.

However, I got to thinking that if I wrote out the matrix in equation form, I'd get

0a + b + 2c + 3d

0a + b + 2c + 5d

0a + 3b + 5c +6d

0 + 0 + 0 + 0

Does the 4x4 matrix equate to the 3x3 matrix

1 2 3

1 2 5

3 5 6 ?

## Homework Equations

(see above for equations)

## The Attempt at a Solution

I'm incline to say no, since the 3x3 matrix would have a determinant, but from the perspective of the equations, I don't see how that are different (at least in terms of the information they convey).

Can anyone explain to me how the two matrices are different? Thanks.