Consider the following statements: S_{1}: The sum of two singular n x n matrices may be non-singular S_{2}: The sum of two n x n non-singular matrices may be singular Which of the following statements is correct?
a)
S_{1} and S_{2} are both true
b)
S_{1} is true, S_{2} is false
c)
S_{1} is flase, S_{2} is true
d)
S_{1} and S_{2} are both false
Correct answer is option 'A'. Can you explain this answer?
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.
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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.