Can I exchange column and then use the row transformation when converting a matrix into a row echelon form? A=[421363472101] 1) C3↔C1 [124343670121] 2) R2=R2−4R1 [12430−5−10−50121] 4−4=0 3−8=−5 6−16=−10 7−12=−5 3) R3=R3+R25 [12430−5−10−50000] 1−1 2−2 1−1 ∴l(A)=2

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Can I exchange column and then use the row transformation when converting a matrix into a row echelon form? A=[421363472101] 1) C3↔C1 [124343670121] 2) R2=R2−4R1 [12430−5−10−50121] 4−4=0 3−8=−5 6−16=−10 7−12=−5 3) R3=R3+R25 [12430−5−10−50000] 1−1 2−2 1−1 ∴l(A)=2

gekraamdbk · Accepted Answer

Step 1  Let  A=[421363472101]=(c1, c2, c3, c4)  where ci is the ith column of A. Observe that c4=c2+c3. So the rank of A is the same as that of  B=[421634210]  Simple row operations gives you  [001004210]  Now it is fairly easy to conclude that the rank must be 2.

Addisyn Thompson · Accepted Answer

Step 1&amp;nbsp;You are permitted to use row and column operations simultaneously when attempting to determine the rank of a matrix.Just a quick correction: what you&#039;re looking for is very different from discovering the matrix&#039;s row echelon form.In fact, there is a very important result in linear algebra that states that : given a&amp;nbsp;m×n&amp;nbsp;matrix A with rank r, then&amp;nbsp;r≤m,&amp;nbsp;r≤n&amp;nbsp;and by means of a finite number of elementary row and column operations, A can be transformed into the matrix&amp;nbsp;[IrO1O2O3]&amp;nbsp;where&amp;nbsp;Ir&amp;nbsp;is the&amp;nbsp;r×r&amp;nbsp;identity matrix and&amp;nbsp;O1,&amp;nbsp;O2&amp;nbsp;and&amp;nbsp;O3&amp;nbsp;are zero matrices.&amp;nbsp;To make it clearer, in your specific example, after applying row and column operations in A we end up in&amp;nbsp;[100001000000]&amp;nbsp;(again, which is not the rref of A). So, rank&amp;nbsp;(A)=2.

RizerMix · Accepted Answer

Mostly no. There are a bunch of theorems about row-equivalent matrices (i.e. matrices that can be transformed to each other with a sequence of row operations) and swapping columns will not make you row-equivalent. The resulting matrix cannot be called a row-echelon form of the original matrix. That said, when finding rank, column operations will also preserve rank, like row operations (as column rank and row rank are always equal). So, the row-echelon form matrix you find, though it doesnt

Can I exchange column and then use the row transformation

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