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UPSC NDA Math Model Paper 10
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© examsnet.com
Question : 91
Total: 120
Find the determinant of the matrix
|
x
−
y
y
−
z
z
−
x
y
−
z
z
−
x
x
−
y
z
−
x
x
−
y
y
−
z
|
x
+
y
+
z
x
2
+
y
2
+
z
2
0
(
x
+
y
+
z
)
2
−
x
y
z
Validate
Solution:
|
x
−
y
y
−
z
z
−
x
y
−
z
z
−
x
x
−
y
z
−
x
x
−
y
y
−
z
|
Apply
R
1
→
R
1
+
R
2
+
R
3
, We get
|
0
0
0
y
−
z
z
−
x
x
−
y
z
−
x
x
−
y
y
−
z
|
As we can see that the entry of the first row is zero.
We know that,
If each entry in any row or column of a determinant is 0, then the value of the determinant is zero.
|
x
−
y
y
−
z
z
−
x
y
−
z
z
−
x
x
−
y
z
−
x
x
−
y
y
−
z
|
=
0
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