4.1--
⎝⎛20240−1625⎠⎞
(i) R1→2R1
⇒ ⎝⎛10220−1325⎠⎞
(ii) R3→R3−2R1
⇒ ⎝⎛10020−532−1⎠⎞
(iii) Interchange 2 and 3 row
⎝⎛1002−503−12⎠⎞
(iv) R2→−5R2
⎝⎛10021030.22⎠⎞
(v) R3→2R3
⎝⎛10021030.21⎠⎞
This is the Row Echelon Form of the matrix.
Since there are 3 non -zero rows hence the Rank is = 3
4.2--
⎝⎛1202−30−412⎠⎞
(i) R2→R2−2R1
⇒ ⎝⎛1002−70−492⎠⎞
(ii) R2→−7R2 ⎝⎛1002−10−4−9/72⎠⎞
⇒ ⎝⎛1002−10−4−9/72⎠⎞
(iii) R3→2R3
⇒ ⎝⎛1002−10−4−9/71⎠⎞
This is the Row Echelon Form of the matrix.
There are 3 non -zero rows hence the rank of the matrix = 3
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