Question
2. Reduce each of the following matrices into Reduced Row Echelon Form. a. (} 1&2&1&2 2&1&2&1 ) b. (} 1&2&1 2&1&2 1&3&1 ) c. (} 1&2&3&1 4&5&6&2 7&8&9&3 )
Solution
4.4
(265 Votos)
Nídia
Mestre · Tutor por 5 anos
Resposta
a. To reduce the matrix
into Reduced Row Echelon Form (RREF), we can perform the following row operations:1. Subtract 2 times the first row from the second row to eliminate the 2 in the first column of the second row:
2. Divide the second row by -3 to make the leading coefficient 1:
3. Subtract 2 times the second row from the first row to eliminate the 2 in the second column of the first row:
The matrix is now in RREF.b. To reduce the matrix
into RREF, we can perform the following row operations:1. Subtract 2 times the first row from the second row to eliminate the 2 in the first column of the second row:
2. Subtract the first row from the third row to eliminate the 1 in the first column of the third row:
3. Divide the second row by -3 to make the leading coefficient 1:
4. Subtract the second row from the third row to eliminate the 1 in the second column of the third row:
The matrix is now in RREF.c. To reduce the matrix
into RREF, we can perform the following row operations:1. Subtract 4 times the first row from the second row to eliminate the 4 in the first column of the second row:
2. Subtract 7 times the first row from the third row to eliminate the 7 in the first column of the third row:
3. Divide the second row by -3 to make the leading coefficient 1:
4. Add 6 times the second row to the third row to eliminate the -6 in the second column of the third row:
The matrix is now in RREF.