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For how many values of k, is the matrix  singular?

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  1. Only one
  2. Only two
  3. Only four
  4. Infinite

Answer (Detailed Solution Below)

Option 4 : Infinite
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Detailed Solution

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Concept:

The matrix is singular if |A| = 0

Calculations:

Given the matrix  singular

We know that the matrix is singular iff |A| = 0

⇒

⇒ 0 - k (k - 5k) + 4 (- k2) = 0

⇒ 4k2 - 4k2 = 0

Therefore, we can take any value of k it makes the matrix singular.

Hence the total value of k is infinite.

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