How can the row rank and column rank be equal here?

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I don't understand how this is equal.

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I can see three pivots so that makes it a rank 3 regarding the columns. Hence, the first three columns are pivot columns, so the matrix has a column rank 3.

But how is the row rank equal to three? To have a row rank of three, shouldn't the entire column 4 consist of [0,0,0,0]? Could someone explain to me what I am missing here?

For me, the definition of a pivot = [1,0,0,0] (so having a one and all others are zero), but when I'd check the row, I can see a [1,0,0,4], which is not equal to what I stated above!

Can someone help me comprehend it? Clearly I am missing something here...