GATE 2010
March 13, 2025GATE 2010
March 13, 2025GATE 2010
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Question 29
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Consider the following matrix 
. If the eigenvalues of A are 4 and 8, then
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x=4, y=10
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x=5, y=8
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x=-3, y=9
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x=-4, y=10
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Question 29 Explanation:
Trace = {Sum of diagonal elements of matrix}
Here given that eigen values are 4, 8
Sum = 8 + 4 = 12
Trace = 2 + y
⇒ 2 + y = 12
y = 10
Determinant = |2y – 3x|
Product of eigen values = 8 × 4 = 32
2y – 3x = 32
(y = 10)
20 – 3x = 32
-12 = 3x
x = -4
∴ x = -4, y = 10
Correct Answer: D
Question 29 Explanation:
Trace = {Sum of diagonal elements of matrix}
Here given that eigen values are 4, 8
Sum = 8 + 4 = 12
Trace = 2 + y
⇒ 2 + y = 12
y = 10
Determinant = |2y – 3x|
Product of eigen values = 8 × 4 = 32
2y – 3x = 32
(y = 10)
20 – 3x = 32
-12 = 3x
x = -4
∴ x = -4, y = 10