Consider the following statements:
S1: The sum of two singular n x n matrices may be non-singular
S2: The sum of two n x n non-singular matrices may be singular
Which of the following statements is correct?
  • a)
    S1 and S2 are both true
  • b)
    S1 is true, S2 is false
  • c)
    S1 is flase, S2 is true
  • d)
    S1 and S2 are both false
Correct answer is option 'A'. Can you explain this answer?

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Answers

Kamla Devi
Jul 21, 2020
S1 is true
Consider two singular matrices

Sum of A and B is given as
However (A + B) is a non-singuiar matrix 
So, S1 is true.
Now, consider two non-singuiar matrices


However (C + D) is a singular matrix. So, S2 is also true.
Therefore, both S1 and S2 are true.

S1 is trueConsider two singular matricesSum of A and B is given asHowever (A + B) is a non-singuiar matrixSo, S1 is true.Now, consider two non-singuiar matricesHowever (C + D) is a singular matrix. So, S2 is also true.Therefore, both S1 and S2 are true.
S1 is trueConsider two singular matricesSum of A and B is given asHowever (A + B) is a non-singuiar matrixSo, S1 is true.Now, consider two non-singuiar matricesHowever (C + D) is a singular matrix. So, S2 is also true.Therefore, both S1 and S2 are true.