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Byju's Answer
Standard XII
Mathematics
Equality of Matrices
Let f x, y =...
Question
Let
f
(
x
,
y
)
=
∣
∣ ∣ ∣
∣
y
−
x
2
x
−
y
2
x
y
−
1
x
−
y
2
x
y
−
1
y
−
x
2
x
y
−
1
y
−
x
2
x
−
y
2
∣
∣ ∣ ∣
∣
find
f
(
2
,
2
)
.
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Solution
f
(
x
,
y
)
=
∣
∣ ∣ ∣
∣
y
−
x
2
x
−
y
2
x
y
−
1
x
−
y
2
x
y
−
1
y
−
x
2
x
y
−
1
y
−
x
2
x
−
y
2
∣
∣ ∣ ∣
∣
f
(
2
,
2
)
=
∣
∣ ∣
∣
−
2
−
2
3
−
2
3
−
2
3
−
2
−
2
∣
∣ ∣
∣
on expanding we get,
=
20
+
20
−
15
=
25
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0
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Q.
Prove that
∣
∣ ∣ ∣
∣
y
z
−
x
2
z
x
−
y
2
x
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Q.
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is divisible by
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)
and hence find the quotient
Q.
If
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∣
y
z
−
x
2
z
x
−
y
2
x
y
−
z
2
x
z
−
y
2
x
y
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y
z
−
x
2
x
y
−
z
2
y
z
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x
2
z
x
−
y
2
∣
∣ ∣ ∣
∣
=
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∣ ∣ ∣
∣
r
2
u
2
u
2
u
2
r
2
u
2
u
2
u
2
r
2
∣
∣ ∣ ∣
∣
, then
Q.
State true or false.
The g
iven equation
∣
∣ ∣ ∣
∣
y
z
−
x
2
z
x
−
y
2
x
y
−
z
2
z
x
−
y
2
x
y
−
z
2
y
z
−
x
2
x
y
−
z
2
y
z
−
x
2
z
x
−
y
2
∣
∣ ∣ ∣
∣
is divisible by
(
x
+
y
+
z
)
.
Q.
Prove that
∣
∣ ∣ ∣
∣
y
z
−
x
2
z
x
−
y
2
x
y
−
z
2
z
x
−
y
2
x
y
−
z
2
y
z
−
x
2
x
y
−
z
2
y
z
−
x
2
z
x
−
y
2
∣
∣ ∣ ∣
∣
is divisible by
(
x
+
y
+
z
)
, and hence find the quotient
OR
Using elementary transformations, find the inverse of the matrix
A
=
⎛
⎜
⎝
8
4
3
2
1
1
1
2
2
⎞
⎟
⎠
and use it to solve the following system of linear equations:
8
x
+
4
y
+
3
z
=
19
2
x
+
y
+
z
=
5
x
+
2
y
+
2
z
=
7
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