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HCU MCA 2013 Paper
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© examsnet.com
Question : 74
Total: 75
Which of the following is equal to the nullity of matrix A below?
A =
[
−
1
4
2
1
3
2
−
2
1
0
2
6
4
]
0
2
1
3
Validate
Solution:
(c) Given matrix,
[
−
1
4
2
1
3
2
−
2
1
0
2
6
4
]
4
×
3
Number of columns (n) = 3
Apply operation,
R
1
→
R
2
A ~
[
1
3
2
−
1
4
2
−
2
1
0
2
6
4
]
Using operations
R
2
→
R
1
+
R
2
,
R
3
→
R
3
+
2
R
1
and
R
4
→
R
4
−
2
R
1
;
A ~
[
1
3
2
0
7
4
0
7
4
0
0
0
]
Again, apply operation,
R
3
→
R
3
−
R
2
A ~
[
1
3
2
0
7
4
0
0
0
0
0
0
]
By Echlon form, Rank of A = f(A)
=
Number of non-zero rows
2
∴ Nullity A = n - f(A) = 3 - 2 = 1.
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