3: Reduce the matrix A(given below) to normal form and hence find its rank 5 0 0 3 8 1 1 A
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Answer:The rank of the matrix is equal to the number of non-zero rows in the matrix after reducing it to the echelon form
Given matrix
A=
⎣
⎢
⎢
⎡
1
1
1
1
1
1
1
1
1
⎦
⎥
⎥
⎤
R
2
→R
2
−R
1
A=
⎣
⎢
⎢
⎡
1
0
1
1
0
1
1
0
1
⎦
⎥
⎥
⎤
R
3
→R
3
−R
1
A=
⎣
⎢
⎢
⎡
1
0
0
1
0
0
1
0
0
⎦
⎥
⎥
⎤
Hence the non-zero row in the above matrix is 1.
Therefore , rank is 1.
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