A = ⎣⎡0022202032−5−6−43291447⎦⎤
Since element at row 1 and column 1 (pivot element) equals 0, we need to swap rows
Then find the first non zero element in the column 1 under the pivot entry
The first non zero element is row 3
Swap rows 1 and 3: ⎣⎡20022020−523−623−494417⎦⎤
make zeros in column 1 except the at entry row 1, column 1 (pivot entry)
Subtract row 1 from row 4
[R4= R4 - R1]; ⎣⎡2000202−2−523−123−474413⎦⎤
Divide row 1 by 2
[R1 = R1/2] ⎣⎡1000102−2−5/223−113−472413⎦⎤
Since element at row 2 and column 2 (pivot element) equals 0, we need to swap rows
Then find the first non zero element in the column 2 under the pivot entry
The first non zero element is row 3
swap rows 2 with 3; ⎣⎡1000120−2−5/232−11−4372143⎦⎤
Make zeros in column 2 except the at entry row 2, column 2 (pivot entry).
Add row 2 to row 4
[R2 =R4 + R2]; ⎣⎡10001200−5/23221−4332144⎦⎤
Divide row 2 by 2
[R2 = R2/2]; ⎣⎡10001100−5/23/2221−23321/244⎦⎤
Subtract row 2 from row 1
[R1 = R1 - R2]; ⎣⎡10000100−43/2223−2333/21/244⎦⎤
Make zeros in column 3 except the at entry row 3, column 3 (pivot entry).
Add row 3 multiplied by 2 to row 1.
[R3 = R1 + (2)R3]; ⎣⎡1000010003/2229−23319/21/244⎦⎤
Subtract row 3 from row 4
[R4 = R4 - R3]; ⎣⎡1000010003/2209−23019/21/240⎦⎤
Divide row 3 by 2
[R3 = R3/2]; ⎣⎡1000010003/2109−23/2019/21/220⎦⎤
Subtract row 3 multiplied by 3/2 to row 2.
[R2 = R2 - (3/2)R3]; ⎣⎡1000010000109−17/43/2019/2−5/220⎦⎤
SINCE ALL ROWS BELOW ARE ZERO THEN THE ANSWER IS,
rref(A)
= ⎣⎡1000010000109−17/43/2019/2−5/220⎦⎤
or in decimal form
= ⎣⎡1000010000109−4.251.509.5−2.520⎦⎤
The rank is = 3
Comments