If A is a 3×3 singular matrix such that λ1=1−i is an eigenvalue of A, then the other eigenvalues of A are 0,1+i

Mathematics

1 answer:

astra-53 [7]2 years ago

5 0

Answer:

1 + i

Step-by-step explanation:

Given that A is a 3 * 3 singular matrix

one of its eigenvalue ( λ1 ) = 1 - i

Given that the determinant of a singular matrix is = 0

therefore the second eigen value ( λ2 ) = 1 + i

1 - i + 1 + i = 0

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Consider "D" the letter to identify distance between A and B

Let's use "t" to identify the time of the first encounter (Devi and Kumar), and create an equation that states that the distance covered by Devi (at 100 m/min) in time "t", is equal to the total distance D minus what Kumar has covered at his speed (80 m/min) in that same time:

Recall that distance equals the speed times the time:

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100 * t = D - 80 * t

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Not, 6 minutes later (at time t+6) , Devi and Li Ting meet .

Then for this encounter the distance covered by Devi equals total distance d minus the distance covered by Li Ting:

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Now, let's equal equation (1) to equation (2), since D should be the same:

180 t = 175 t + 150