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Identify the following matrix is singular or non-singular? [5,0,5,1,99,100,6,99,105]

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Question

Identify the following matrix is singular or non-singular?

`[(5, 0, 5),(1, 99, 100),(6, 99, 105)]`

Sum
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Solution

Let A = `[(5, 0, 5),(1, 99, 100),(6, 99, 105)]`

∴ |A| = `|(5, 0, 5),(1, 99, 100),(6, 99, 105)|`

Applying C2 → C1 + C2, we get

|A| = `|(5, 5, 5),(1, 100, 100),(6, 105, 105)|`

= 0    ...[∵ C2 and C3 are identical]

∴ A is a singular matrix.

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Chapter 4: Determinants and Matrices - Exercise 4.4 [Page 83]

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