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Question

Consider the following 2 x 2 matrix A where two elements are unknown and are marked by a and b. The eigen values of this matrix are - 1 and 7. What are the values of a and b? A=[14ba]

A
a=6,b=4
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B
a=4,b=6
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C
a=3,b=5
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D
a=5,b=3
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Solution

The correct option is D a=5,b=3
Given that A=[14ba] has given values -1 and 7.

So Trace (A) =λ1+λ2 and |A|=λ1.λ2
a+1=1+7
and a4b=(1)(7)
a=5
and b=3

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