Linear Algebra | Reduced Row Echelon | Best Explanation With Animation

Friends, in this video, we are going to discuss reduced row echelon form. It is a form of matrix which satisfy the following conditions. First condition, there is a zero row, then it should at the bottom of the matrix. So here we have zero row, it should at bottom of the matrix. That means there is no non-zero below this zero row. So it should be in this form, then it satisfy the condition. then there is a no non-zero below this zero row. Second condition if there is a non-zero then first non-zero entry should be 1 which is called the leading one of the row. So we have first three non-zero then the green star entry are the leading entries because rows start from left to right. This first non-zero entry should be 1 and which is called the leading one of the row. Third condition if there is a two consecutive non-zero row then below row should have more zero than the above row before leading one. So we have three consecutive non-zero row. In the first row there is a 0 0 before the leading one. In the second row there is a 2 0 before the leading one and in the third row there is a 1 0 before the leading one. So by the condition first and second row satisfy the condition because below row is second row which has two zero which is more than the first row because first row is zero zero before the leading one and the second and third row third row has one zero before the leading one and second row has two zero before the leading one so this two row does not satisfy the condition and it should in this position then satisfy the condition number three now condition 4 in the column of leading one all other entry should be 0 except the leading one so we have three column of leading one then in the first column except the leading one all the entries are 0 in the second and third column these star entries and this star entry should be 0 then it satisfies the fourth condition and a matrix will satisfy all the four condition it is in the reduced row echelon form now example is the following matrix is in the reduced row echelon form so we are going to check one by one condition first condition there is a zero row should at the bottom but there is a non-zero below the zero row therefore it does not satisfy the first condition and hence the matrix not in the reduced row echelon form example number two first condition 0 row should at the bottom correct it satisfy the first condition leading one concept so first non-zero as leading one second non-zero first non-zero entry is one so it satisfy the condition in the third row first non-zero entry is two in place of one so it does not satisfy the condition and the second condition is violated therefore a is not in the reduced row echelon form example number three first condition zero row should at the bottom correct second condition leading one so first row begin with the leading one second row first non-zero entry is one and the third row first non-zero entry is one so satisfy the second condition third condition for two consecutive non-zero second row has more zero than the first row first second and third row so in the first row zero zero before the leading one in the second row one zero before the leading one and the third row zero zero before the leading one so first and second row satisfy that the below row has more zero than the above row but in the second and third row third row has zero zeros and the second row has one zero so it does not satisfy the third condition and hence this matrix is not in the reduced row echelon form fourth example first condition zero row should at the bottom correct second condition leading one yes first second and third row begin with the leading one third condition two consecutive non-zero so first row is 0 0 second row is 1 0 and the third row is 2 0 before the leading one therefore they satisfy the third condition now the fourth condition in the column of leading one all the entries 0 except the leading one so in the first column all the entries are zero except the one in the second and third column we have one and minus one they are non-zero entries therefore they does not satisfy the fourth condition hence this matrix is not in the reduced row echelon form example number five first condition zero row should at the bottom which is correct leading one which is also correct before the leading one there is a more 0 in the below row so for the first second and third row 0 0s in the first row 1 0 in the second row and 2 0 in the third row before the leading one and they satisfy the third condition fourth condition in the column of leading one other entry should be 0 so we have three columns with the leading one first column all the entries are 0 second column all the entries are 0 and the third column all the entries are 0 except the leading one therefore fourth condition is also satisfied by the matrix and hence it is in the reduced row echelon form thanks for watching for more videos like share subscribe press the bell icon of next channel