What is the value of the determinant |15 -5/3 | |√3 3/5| (A) O (B) 30 (C) 15 (D) - 30
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Let Δ=
∣
∣
∣
∣
∣
∣
∣
∣
13
+
3
15
+
26
3+
65
2
5
5
15
5
10
5
∣
∣
∣
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
∣
∣
∣
3
15
3
2
5
5
15
5
10
5
∣
∣
∣
∣
∣
∣
∣
∣
+
∣
∣
∣
∣
∣
∣
∣
∣
13
26
65
2
5
5
15
5
10
5
∣
∣
∣
∣
∣
∣
∣
∣
Taking common from 1st determinant
3
,
5
,
5
from C
1
,C
2
,C
3
respectively and
Taking common from 2nd determinant
13
,
5
,
5
from C
1
,C
2
,C
3
respectively, we get
=
3
×
5
×
5
∣
∣
∣
∣
∣
∣
∣
∣
1
5
3
2
5
3
1
2
5
∣
∣
∣
∣
∣
∣
∣
∣
+
13
×
5
×
5
∣
∣
∣
∣
∣
∣
∣
∣
1
2
5
2
5
3
1
2
5
∣
∣
∣
∣
∣
∣
∣
∣
=
3
×5
∣
∣
∣
∣
∣
∣
∣
∣
1
5
3
2
5
3
1
2
5
∣
∣
∣
∣
∣
∣
∣
∣
+0 (∵C
1
and C
2
are indentical)
=5
3
∣
∣
∣
∣
∣
∣
∣
∣
1
5
3
2
5
3
1
2
5
∣
∣
∣
∣
∣
∣
∣
∣
Applying C
2
→C
2
−C
1
∴Δ=5
3
∣
∣
∣
∣
∣
∣
∣
∣
1
5
3
1
0
0
1
2
5
∣
∣
∣
∣
∣
∣
∣
∣
Expanding along C
2
∴Δ=5
3
⋅(01)
∣
∣
∣
∣
∣
∣
5
3
2
5
∣
∣
∣
∣
∣
∣
=−5
3
(5−
6
)
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